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Sample records for sequential feynman integrals

  1. A recursive reduction of tensor Feynman integrals

    International Nuclear Information System (INIS)

    Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

    2009-07-01

    We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

  2. Feynman integral calculus

    CERN Document Server

    Smirnov, Vladimir A

    2006-01-01

    The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. `Feynman Integral Calculus' characterizes the most powerful methods in a systematic way. It concentrates on the methods that have been employed recently for most sophisticated calculations and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. It also shows how to choose adequate methods and combine them in a non-trivial way. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated.

  3. Probing finite coarse-grained virtual Feynman histories with sequential weak values

    Science.gov (United States)

    Georgiev, Danko; Cohen, Eliahu

    2018-05-01

    Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

  4. Feynman integrals and hyperlogarithms

    Energy Technology Data Exchange (ETDEWEB)

    Panzer, Erik

    2015-02-05

    We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ{sup 4} theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

  5. Feynman integrals and hyperlogarithms

    International Nuclear Information System (INIS)

    Panzer, Erik

    2015-01-01

    We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the ε-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless φ 4 theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by the √(3)). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.

  6. Baikov-Lee representations of cut Feynman integrals

    International Nuclear Information System (INIS)

    Harley, Mark; Moriello, Francesco; Schabinger, Robert M.

    2017-01-01

    We develop a general framework for the evaluation of d-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy’s residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.

  7. Feynman integral calculus

    International Nuclear Information System (INIS)

    Smirnov, V.A.

    2006-01-01

    The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. (orig.)

  8. Feynman integral calculus

    Energy Technology Data Exchange (ETDEWEB)

    Smirnov, V.A. [Lomonosov Moscow State Univ. (Russian Federation). Skobeltsyn Inst. of Nuclear Physics

    2006-07-01

    The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. (orig.)

  9. Mathematical aspects of Feynman integrals

    International Nuclear Information System (INIS)

    Bogner, Christian

    2009-08-01

    In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

  10. Mathematical aspects of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Bogner, Christian

    2009-08-15

    In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

  11. Analytic tools for Feynman integrals

    International Nuclear Information System (INIS)

    Smirnov, Vladimir A.

    2012-01-01

    Most powerful methods of evaluating Feynman integrals are presented. Reader will be able to apply them in practice. Contains numerous examples. The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author's previous Springer book ''Evaluating Feynman Integrals'' and its textbook version ''Feynman Integral Calculus.'' Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, ''Applied Asymptotic Expansions in Momenta and Masses,'' by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.

  12. Analytic Tools for Feynman Integrals

    CERN Document Server

    Smirnov, Vladimir A

    2012-01-01

    The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice.  This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added:  One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on t...

  13. Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Bergbauer, Christoph

    2009-06-11

    The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

  14. Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

    International Nuclear Information System (INIS)

    Bergbauer, Christoph

    2009-01-01

    The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

  15. Analytic tools for Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Smirnov, Vladimir A. [Moscow State Univ. (Russian Federation). Skobeltsyn Inst. of Nuclear Physics

    2012-07-01

    Most powerful methods of evaluating Feynman integrals are presented. Reader will be able to apply them in practice. Contains numerous examples. The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author's previous Springer book ''Evaluating Feynman Integrals'' and its textbook version ''Feynman Integral Calculus.'' Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, ''Applied Asymptotic Expansions in Momenta and Masses,'' by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.

  16. A note on relativistic Feynman-type integrals

    International Nuclear Information System (INIS)

    Namsrai, Kh.

    1979-01-01

    An attempt is made to generalize the definition of Feynman path integral to the relativistic case within the framework of the Kershaw stochastic model. The Smoluchowski type equations are used which allow one to obtain easily the Schrodinger, Klein-Gordon and Dirac equations. The interaction is introduced by using Weyl's gaude theory. In the model developed the Feynman process may formally by interpreted as a stochastic diffusion process in complex times with a real probability measure which occurs in the Euclidean space. Feynman path integrals themselves are not obtained in the model, nonetheless it represents an interest as one of possibilities of the relativistic generalization of Feynman type integrals

  17. Some recent results on evaluating Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Smirnov, V.A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

    2006-07-15

    Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve integration by parts relations in an automatic way is described.

  18. Some recent results on evaluating Feynman integrals

    International Nuclear Information System (INIS)

    Smirnov, V.A.

    2006-01-01

    Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve integration by parts relations in an automatic way is described

  19. Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

    Energy Technology Data Exchange (ETDEWEB)

    Butko, Yana A., E-mail: yanabutko@yandex.ru, E-mail: kinderknecht@math.uni-sb.de [Bauman Moscow State Technical University, 2nd Baumanskaya street, 5, Moscow 105005, Russia and University of Saarland, Postfach 151150, D-66041 Saarbrücken (Germany); Grothaus, Martin, E-mail: grothaus@mathematik.uni-kl.de [University of Kaiserslautern, 67653 Kaiserslautern (Germany); Smolyanov, Oleg G., E-mail: Smolyanov@yandex.ru [Lomonosov Moscow State University, Vorob’evy gory 1, Moscow 119992 (Russian Federation)

    2016-02-15

    Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures.

  20. Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions

    International Nuclear Information System (INIS)

    Butko, Yana A.; Grothaus, Martin; Smolyanov, Oleg G.

    2016-01-01

    Evolution semigroups generated by pseudo-differential operators are considered. These operators are obtained by different (parameterized by a number τ) procedures of quantization from a certain class of functions (or symbols) defined on the phase space. This class contains Hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the Lévy-Khintchine formula. The considered semigroups are represented as limits of n-fold iterated integrals when n tends to infinity. Such representations are called Feynman formulae. Some of these representations are constructed with the help of another pseudo-differential operator, obtained by the same procedure of quantization; such representations are called Hamiltonian Feynman formulae. Some representations are based on integral operators with elementary kernels; these are called Lagrangian Feynman formulae. Langrangian Feynman formulae provide approximations of evolution semigroups, suitable for direct computations and numerical modeling of the corresponding dynamics. Hamiltonian Feynman formulae allow to represent the considered semigroups by means of Feynman path integrals. In the article, a family of phase space Feynman pseudomeasures corresponding to different procedures of quantization is introduced. The considered evolution semigroups are represented as phase space Feynman path integrals with respect to these Feynman pseudomeasures, i.e., different quantizations correspond to Feynman path integrals with the same integrand but with respect to different pseudomeasures. This answers Berezin’s problem of distinguishing a procedure of quantization on the language of Feynman path integrals. Moreover, the obtained Lagrangian Feynman formulae allow also to calculate these phase space Feynman path integrals and to connect them with some functional integrals with respect to probability measures

  1. Feynman maps without improper integrals

    International Nuclear Information System (INIS)

    Exner, P.; Kolerov, G.I.

    1980-01-01

    The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-inteo-rable functions in the sense of Albeverio and Hoegh-Krohn. The original definition of the F-maps is slightly modified: it is started from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F 1 -map (or Feynman integral); this fact is of a certain importance for classical limit of quantum mechanics

  2. Numerical evaluation of tensor Feynman integrals in Euclidean kinematics

    Energy Technology Data Exchange (ETDEWEB)

    Gluza, J.; Kajda [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, T.; Yundin, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2010-10-15

    For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two algorithms for this purpose which may be applied in the Euclidean kinematical region and in d=4-2{epsilon} dimensions. One method uses Mellin-Barnes representations for the Feynman parameter representation of multi-loop Feynman integrals with arbitrary tensor rank. Our Mathematica package AMBRE has been extended for that purpose, and together with the packages MB (M. Czakon) or MBresolve (A. V. Smirnov and V. A. Smirnov) one may perform automatically a numerical evaluation of planar tensor Feynman integrals. Alternatively, one may apply sector decomposition to planar and non-planar multi-loop {epsilon}-expanded Feynman integrals with arbitrary tensor rank. We automatized the preparations of Feynman integrals for an immediate application of the package sectordecomposition (C. Bogner and S. Weinzierl) so that one has to give only a proper definition of propagators and numerators. The efficiency of the two implementations, based on Mellin-Barnes representations and sector decompositions, is compared. The computational packages are publicly available. (orig.)

  3. Rigorous time slicing approach to Feynman path integrals

    CERN Document Server

    Fujiwara, Daisuke

    2017-01-01

    This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved. The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by...

  4. Feynman integrals in QCD made simple

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    A key insight is that important properties of these functions can be predicted by inspecting the singularity structure of the Feynman integrand. Combined with the differential equations technique, this gives a powerful method for computing the necessary Feynman integrals. I will review these ideas, based on Phys.Rev.Lett. 110 (2013) 25, and present recent new results relevant for QCD scattering amplitudes.

  5. New framework for the Feynman path integral

    International Nuclear Information System (INIS)

    Shaharir, M.Z.

    1986-01-01

    The well-known Fourier integral solution of the free diffusion equation in an arbitrary Euclidean space is reduced to Feynmannian integrals using the method partly contained in the formulation of the Fresnelian integral. By replacing the standard Hilbert space underlying the present mathematical formulation of the Feynman path integral by a new Hilbert space, the space of classical paths on the tangent bundle to the Euclidean space (and more general to an arbitrary Riemannian manifold) equipped with a natural inner product, we show that our Feynmannian integral is in better agreement with the qualitative features of the original Feynman path integral than the previous formulations of the integral

  6. Algorithm FIRE-Feynman Integral REduction

    International Nuclear Information System (INIS)

    Smirnov, A.V.

    2008-01-01

    The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating explicitly over loop momenta when possible. Currently it is being used in complicated three-loop calculations.

  7. Applying Groebner bases to solve reduction problems for Feynman integrals

    International Nuclear Information System (INIS)

    Smirnov, Alexander V.; Smirnov, Vladimir A.

    2006-01-01

    We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential

  8. Applying Groebner bases to solve reduction problems for Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Smirnov, Alexander V. [Mechanical and Mathematical Department and Scientific Research Computer Center of Moscow State University, Moscow 119992 (Russian Federation); Smirnov, Vladimir A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

    2006-01-15

    We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential.

  9. Feynman integrals and the moment problem

    International Nuclear Information System (INIS)

    Pusterla, M.; Turchetti, G.; Vitali, G.

    1976-01-01

    In this letter it is illustrated a general procedure, based on the momentum method, to estimate the scalar Feynman integrals. In order to illustrate the various situations discussed, some numerical examples are presented

  10. Solving recurrence relations for multi-loop Feynman integrals

    International Nuclear Information System (INIS)

    Smirnov, Vladimir A.; Steinhauser, Matthias

    2003-01-01

    We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, i.e., the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov [Phys. Lett. B 385 (1996) 404, Nucl. Instrum. Methods A 389 (1997) 347] can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential

  11. Feynman path integral and the interaction picture

    International Nuclear Information System (INIS)

    Pugh, R.E.

    1986-01-01

    The role of interaction-picture fields in the construction of coherent states and in the derivation of the Feynman path integral for interacting scalar quantum fields is examined. Special attention is paid to the dependence of the integrand on the intermediate times and it is shown that the Feynman rules are valid prior to taking the limit wherein the number of intermediate times goes to infinity; thus, this number does not act as a cutoff in divergent amplitudes. Specific normalization factors are determined

  12. Cuts of Feynman Integrals in Baikov representation

    Energy Technology Data Exchange (ETDEWEB)

    Frellesvig, Hjalte; Papadopoulos, Costas G. [Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’,P.O. Box 60037, Agia Paraskevi, 15310 (Greece)

    2017-04-13

    Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

  13. Cuts of Feynman Integrals in Baikov representation

    International Nuclear Information System (INIS)

    Frellesvig, Hjalte; Papadopoulos, Costas G.

    2017-01-01

    Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in d dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

  14. Equivariance, Variational Principles, and the Feynman Integral

    Directory of Open Access Journals (Sweden)

    George Svetlichny

    2008-03-01

    Full Text Available We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman's integral.

  15. Lectures on differential equations for Feynman integrals

    International Nuclear Information System (INIS)

    Henn, Johannes M

    2015-01-01

    Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE. (topical review)

  16. arXiv Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

    CERN Document Server

    Abreu, Samuel; Duhr, Claude; Gardi, Einan

    2017-12-15

    We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent expansion in the dimensional regulator are multiple polylogarithms (MPLs). Our main result is the conjecture that this diagrammatic coaction reproduces the combinatorics of the coaction on MPLs order by order in the Laurent expansion. We show that our conjecture holds in a broad range of nontrivial one-loop integrals. We then explore its consequences for the study of discontinuities of Feynman integrals, and the differential equations that they satisfy. In particular, using the diagrammatic coaction along with information from cuts, we explicitly derive differential equations for any one-loop Feynman integral. We also explain how to construct the symbol of any one-loop Feynman integral recursively. Finally, we show that our diagrammatic coaction follows, in the special case of o...

  17. Mathematical theory of Feynman path integrals an introduction

    CERN Document Server

    Albeverio, Sergio A; Mazzucchi, Sonia

    2008-01-01

    Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. To take care of the many developments since then, an entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

  18. Systematic approximation of multi-scale Feynman integrals arXiv

    CERN Document Server

    Borowka, Sophia; Hulme, Daniel

    An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop three-point and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.

  19. Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

    Science.gov (United States)

    Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

    2017-04-07

    In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

  20. Connection between Feynman integrals having different values of the space-time dimension

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    1996-05-01

    A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension d is proposed. The relation between d and d-2 dimensional integrals is given in terms of a differential operator for which an explicit formula can be obtained for each Feynman diagram. We show how the method works for one-, two- and three-loop integrals. The new recurrence relations w.r.t. d are complementary to the recurrence relations which derive from the method of integration by parts. We find that the problem of the irreducible numerators in Feynman integrals can be naturally solved in the framework of the proposed generalized recurrence relations. (orig.)

  1. S-bases as a tool to solve reduction problems for Feynman integrals

    International Nuclear Information System (INIS)

    Smirnov, A.V.; Smirnov, V.A.

    2006-01-01

    We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined

  2. S-bases as a tool to solve reduction problems for Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Smirnov, A.V. [Scientific Research Computing Center of Moscow State University, Moscow 119992 (Russian Federation); Smirnov, V.A. [Nuclear Physics Institute of Moscow State University, Moscow 119992 (Russian Federation)

    2006-10-15

    We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a recently suggested reduction algorithm which uses Groebner bases. New results obtained with its help for a family of three-loop Feynman integrals are outlined.

  3. The algebraic locus of Feynman integrals

    OpenAIRE

    Kol, Barak

    2016-01-01

    In the Symmetries of Feynman Integrals (SFI) approach, a diagram's parameter space is foliated by orbits of a Lie group associated with the diagram. SFI is related to the important methods of Integrations By Parts and of Differential Equations. It is shown that sometimes there exist a locus in parameter space where the set of SFI differential equations degenerates into an algebraic equation, thereby enabling a solution in terms of integrals associated with degenerations of the diagram. This i...

  4. Feynman integrals and difference equations

    International Nuclear Information System (INIS)

    Moch, S.; Schneider, C.

    2007-09-01

    We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

  5. Picard-Fuchs equations of dimensionally regulated Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Zayadeh, Raphael

    2013-12-15

    This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is

  6. Picard-Fuchs equations of dimensionally regulated Feynman integrals

    International Nuclear Information System (INIS)

    Zayadeh, Raphael

    2013-12-01

    This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is the two

  7. Feynman integrals and difference equations

    Energy Technology Data Exchange (ETDEWEB)

    Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation

    2007-09-15

    We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)

  8. A complete algebraic reduction of one-loop tensor Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2010-09-15

    Guided by the need to eliminate inverse Gram determinants (){sub 5} from tensorial 5-point functions and sub-Gram determinants (){sub 4} from tensorial 4-point functions, we set up a new and very efficient approach for the tensor reduction of Feynman integrals. We eliminate all Gram determinants for one-loop 5-point integrals up to tensors of rank R=5 by reducing their tensor coefficients to higherdimensional 4-point tensor coefficients. These in turn are reduced to expressions which are free of inverse powers of (){sub 4}, but depend on higher-dimensional integrals I{sub 4}{sup (d)} with d{<=}2R. Their expression in terms of scalar integrals defined in the generic dimension, I{sub 4}; I{sub 3}; I{sub 2}; I{sub 1}, however, introduces coefficients [1=(){sub 4}]{sup R} for tensors of rank R. For small or vanishing (){sub 4}, an efficient expansion is found so that a stable numerical evaluation of massive and massless Feynman integrals at arbitrary values of the Gram determinants is made possible. Finally, some relations are mentioned which may be useful for analytic simplifications of the original Feynman diagrams. (orig.)

  9. Feynman Integrals with Absorbing Boundaries

    OpenAIRE

    Marchewka, A.; Schuss, Z.

    1997-01-01

    We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region. Trajectories that reach the absorbing wall are discounted from the population of the surviving trajectories with a certain weighting factor. Under the assumption that absorbed trajectories do not interfere with the surviving trajectories, we obtain a time dependent absorption law. Two examples are worked ...

  10. Quantum gravitation. The Feynman path integral approach

    International Nuclear Information System (INIS)

    Hamber, Herbert W.

    2009-01-01

    The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for both perturbative as well as non-perturbative studies, and is known to already provide a framework of choice for the theoretical investigation of non-abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman's formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. Later the lattice formulation of gravity is presented as an essential tool towards an understanding of key features of the non-perturbative vacuum. The book ends with a discussion of contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe. (orig.)

  11. Feynman path integrals - from the prodistribution definition to the calculation of glory scattering

    International Nuclear Information System (INIS)

    DeWitt-Morette, C.

    1984-01-01

    In these lectures I present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals. I propose to compute the glory scattering of gravitational waves by black holes. (orig./HSI)

  12. Asymptotic behaviour of Feynman integrals

    International Nuclear Information System (INIS)

    Bergere, M.C.

    1980-01-01

    In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)

  13. The ε-form of the differential equations for Feynman integrals in the elliptic case

    Science.gov (United States)

    Adams, Luise; Weinzierl, Stefan

    2018-06-01

    Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

  14. Shifts of integration variable within four- and N-dimensional Feynman integrals

    International Nuclear Information System (INIS)

    Elias, V.; McKeon, G.; Mann, R.B.

    1983-01-01

    We resolve inconsistencies between integration in four dimensions, where shifts of integration variable may lead to surface terms, and dimensional regularization, where no surface terms accompany such shifts, by showing that surface terms arise only for discrete values of the dimension parameter. General formulas for variable-of-integration shifts within N-dimensional Feynman integrals are presented, and the VVA triangle anomaly is interpreted as a manifestation of surface terms occurring in exactly four dimensions

  15. Computer generation of integrands for Feynman parametric integrals

    International Nuclear Information System (INIS)

    Cvitanovic, Predrag

    1973-01-01

    TECO text editing language, available on PDP-10 computers, is used for the generation and simplification of Feynman integrals. This example shows that TECO can be a useful computational tool in complicated calculations where similar algebraic structures recur many times

  16. Transport coefficients for deeply inelastic scattering from the Feynman path integral method

    International Nuclear Information System (INIS)

    Brink, D.M.; Neto, J.; Weidenmueller, H.A.

    1979-01-01

    Friction and diffusion coefficients can be derived simply by combining statistical arguments with the Feynman path integral method. A transport equation for Feynman's influence functional is obtained, and transport coefficients are deduced from it. The expressions are discussed in the limits of weak, and of strong coupling. (Auth.)

  17. Solving differential equations for Feynman integrals by expansions near singular points

    Science.gov (United States)

    Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

    2018-03-01

    We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

  18. AMBRE - a mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Gluza, J.; Kajda, K. [Silesia Univ, Katowice (Poland). Dept. of Field Theory and Particle Physics, Inst. of Phsyics; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2007-05-15

    The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2{epsilon} dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in {epsilon}. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops. (orig.)

  19. A practical criterion of irreducibility of multi-loop Feynman integrals

    International Nuclear Information System (INIS)

    Baikov, P.A.

    2006-01-01

    A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial

  20. Feynman path integral formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Mizrahi, M.M.

    1975-01-01

    The subject of this investigation is Feynman's path integral quantization scheme, which is a powerful global formalism with great intuitive appeal. It stems from the simple idea that a probability amplitude for a system to make a transition between two states is the ''sum'' of the amplitudes for all the possible ways the transition can take place

  1. Advanced computer algebra algorithms for the expansion of Feynman integrals

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Round, Mark; Schneider, Carsten

    2012-10-01

    Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ε-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

  2. Advanced computer algebra algorithms for the expansion of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2012-10-15

    Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

  3. Polygonal-path approximation on the path spaces of quantum mechanical systems: extended Feynman maps

    International Nuclear Information System (INIS)

    Exner, R.; Kolerov, G.I.

    1981-01-01

    Various types of polygonal-path approximations appearing in the functional-integration theory are discussed. The uniform approximation is applied to extend the definition of the Feynman maps from our previous paper and to prove consistency of this extension. Relations of the extended Fsub(-i)-map to the Wiener integral are given. In particular, the basic theorem about the sequential Wiener integral by Cameron is improved [ru

  4. Path-integral quantization of solitons using the zero-mode Feynman rule

    International Nuclear Information System (INIS)

    Sung Sheng Chang

    1978-01-01

    We propose a direct expansion treatment to quantize solitons without collective coordinates. Feynman's path integral for a free particle subject to an external force is directly used as the generating functional for the zero-frequency mode. The generating functional has no infrared singularity and defines a zero-mode Feynman rule which also gives a correct perturbative expansion for the harmonic-oscillator Green's function by treating the quadratic potential as a perturbation. We use the zero-mode Feynman rule to calculate the energy shift due to the second-order quantum corrections for solitons. Our result agrees with previous predictions using the collective-coordinate method or the method of Goldstone and Jackiw

  5. Feynman's path integrals and Bohm's particle paths

    International Nuclear Information System (INIS)

    Tumulka, Roderich

    2005-01-01

    Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. (letters and comments)

  6. Feynman path integral related to stochastic schroedinger equation

    International Nuclear Information System (INIS)

    Belavkin, V.P.; Smolyanov, O.G.

    1998-01-01

    The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru

  7. Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

    International Nuclear Information System (INIS)

    Rezende, J.

    1983-01-01

    We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

  8. The power counting theorem for Feynman integrals with massless propagators

    International Nuclear Information System (INIS)

    Lowenstein, J.H.

    2000-01-01

    Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.)

  9. The power counting theorem for Feynman integrals with massless propagators

    International Nuclear Information System (INIS)

    Lowenstein, J.H.

    1975-01-01

    Dyson's power counting theorem is extended to the case where some of the mass parameters vanish. Weinberg's ultraviolet convergence conditions are supplemented by infrared convergence conditions which combined are sufficient for the convergence of Feynman integrals. (orig.) [de

  10. Automatic numerical integration methods for Feynman integrals through 3-loop

    International Nuclear Information System (INIS)

    De Doncker, E; Olagbemi, O; Yuasa, F; Ishikawa, T; Kato, K

    2015-01-01

    We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QuadPack accommodates boundary singularities of fairly general types. PARINT is a package for multivariate integration layered over MPI (Message Passing Interface), which runs on clusters and incorporates advanced parallel/distributed techniques such as load balancing among processes that may be distributed over a network of nodes. Results are included for 3-loop self-energy diagrams without IR (infra-red) or UV (ultra-violet) singularities. A procedure based on iterated integration and extrapolation yields a novel method of numerical regularization for integrals with UV terms, and is applied to a set of 2-loop self-energy diagrams with UV singularities. (paper)

  11. Convergence theorems for renormalized Feynman integrals with zero-mass propagators

    International Nuclear Information System (INIS)

    Lowenstein, J.H.

    1976-01-01

    A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions for a wide class of theories with zero-mass propagators. (orig.) [de

  12. An approach to the calculation of many-loop massless Feynman integrals

    International Nuclear Information System (INIS)

    Gorishnii, S.G.; Isaev, A.P.

    1985-01-01

    A generalization of the identity of dimensionless regular-zation is proposed. The generalization is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals with one external momentum into classes of equal integrals, and also for calculating some of them. A nontrivial symmetry of the propagator integrals is revealed, on the basis of which a complete system of functional equations for determining two-loop integrals is derived. Possible generalizations of these equations are discussed

  13. A power counting theorem for Feynman integrals on the lattice

    International Nuclear Information System (INIS)

    Reisz, T.

    1988-01-01

    A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introduced, which allows the formulation of the theorem in terms of power counting conditions. (orig.)

  14. Complete algebraic reduction of one-loop tensor Feynman integrals

    International Nuclear Information System (INIS)

    Fleischer, J.; Riemann, T.

    2011-01-01

    We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.

  15. Summing over Feynman histories by functional contour integration

    International Nuclear Information System (INIS)

    Garrison, J.C.; Wright, E.M.

    1986-01-01

    The authors show how complex paths can be consistently introduced into sums for Feynman histories by using the notion of functional contour integration. For a kappa-dimensional system specified by a potential with suitable analyticity properties, each coordinate axis is replaced by a copy of the complex plane, and at each instant of time a contour is chosen in each plane. This map from the time axis into the set of complex contours defines a functional contour. The family of contours labelled by time generates a (kappa+1)-dimensional submanifold of the (2kappa+1)-dimensional space defined by the cartesian product of the time axis and the coordinate planes. The complex Feynman paths lie on this submanifold. An application of this idea to systems described by absorptive potentials yields a simple derivation of the correct WKB result in terms of a complex path that extremalises the action. The method can also be applied to spherically symmetric potentials by using a partial wave expansion and restricting the contours appropriately. (author)

  16. A symbolic summation approach to Feynman integral calculus

    International Nuclear Information System (INIS)

    Bluemlein, Johannes; Klein, Sebastian

    2010-11-01

    Given a Feynman parameter integral, depending on a single discrete variable N and a real parameter ε, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in ε. In a first step, the integrals are expressed by hypergeometric multi sums by means of symbolic transformations. Given this sum format, we develop new summation tools to extract the first coefficients of its series expansion whenever they are expressible in terms of indefinite nested product-sum expressions. In particular, we enhance the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and we present new algorithms to find formal Laurent series solutions of a given recurrence relation. (orig.)

  17. A symbolic summation approach to Feynman integral calculus

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [Technische Hochschule Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie; Schneider, Carsten; Stan, Flavia [Johannes Kepler Univ. Linz (AT). Research Inst. for Symbolic Computation (RISC)

    2010-11-15

    Given a Feynman parameter integral, depending on a single discrete variable N and a real parameter {epsilon}, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in {epsilon}. In a first step, the integrals are expressed by hypergeometric multi sums by means of symbolic transformations. Given this sum format, we develop new summation tools to extract the first coefficients of its series expansion whenever they are expressible in terms of indefinite nested product-sum expressions. In particular, we enhance the known multi-sum algorithms to derive recurrences for sums with complicated boundary conditions, and we present new algorithms to find formal Laurent series solutions of a given recurrence relation. (orig.)

  18. The Feynman integral for time-dependent anharmonic oscillators

    International Nuclear Information System (INIS)

    Grothaus, M.; Khandekar, D.C.; da Silva, J.L.; Streit, L.

    1997-01-01

    We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution. copyright 1997 American Institute of Physics

  19. On application of analytical transformation system using a computer for Feynman intearal calculation

    International Nuclear Information System (INIS)

    Gerdt, V.P.

    1978-01-01

    Various systems of analytic transformations for the calculation of Feynman integrals using computers are discussed. The hyperspheric technique Which is used to calculate Feynman integrals enables to perform angular integration for a set of diagrams, thus reducing the multiplicity of integral. All calculations based on this method are made with the ASHMEDAL program. Feynman integrals are calculated in Euclidean space using integration by parts and some differential identities. Analytic calculation of Feynman integral is performed by the MACSYMA system. Dispersion method of integral calculation is implemented in the SCHOONSCHIP system, calculations based on features of Nielsen function are made using efficient SINAC and RSIN programs. A tube of basic Feynman integral parameters calculated using the above techniques is given

  20. Numerical calculations in elementary quantum mechanics using Feynman path integrals

    International Nuclear Information System (INIS)

    Scher, G.; Smith, M.; Baranger, M.

    1980-01-01

    We show that it is possible to do numerical calculations in elementary quantum mechanics using Feynman path integrals. Our method involves discretizing both time and space, and summing paths through matrix multiplication. We give numerical results for various one-dimensional potentials. The calculations of energy levels and wavefunctions take approximately 100 times longer than with standard methods, but there are other problems for which such an approach should be more efficient

  1. Feynman rules and generalized ward identities in phase space functional integral

    International Nuclear Information System (INIS)

    Li Ziping

    1996-01-01

    Based on the phase-space generating functional of Green function, the generalized canonical Ward identities are derived. It is point out that one can deduce Feynman rules in tree approximation without carrying out explicit integration over canonical momenta in phase-space generating functional. If one adds a four-dimensional divergence term to a Lagrangian of the field, then, the propagator of the field can be changed

  2. Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation

    International Nuclear Information System (INIS)

    Gonzalez, Ivan; Schmidt, Ivan

    2007-01-01

    We present an improved form of the integration technique known as NDIM (negative dimensional integration method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a φ 3 +φ 4 theory in D=4-2ε dimensions, considering generic topologies of L loops and E independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n-1), where n is the number of energy scales present in the diagram

  3. Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral

    CERN Document Server

    Hose, R D

    2006-01-01

    Using the separation of the variables technique, the free particle solutions of the Dirac equation in the momentum space are shown to be actually providing the definition of Delta function for the Schr dinger picture. Further, the said solution is shown to be derivable on the sole strength of geometrical argument that the Dirac equation for free particle is an equation of a plane in momentum space. During the evolution of time in the Schr dinger picture, the normal to the said Dirac equation plane is shown to be constantly changing in direction due to the uncertainty principle and thereby, leading to a zigzag path for the Dirac particle in the momentum space. Further, the time evolution of the said Delta function solutions of the Dirac equation is shown to provide Feynman integral of all such zigzag paths in the momentum space. Towards the end of the paper, Feynman path integral between two fixed spatial points in the co-ordinate space during a certain time interv! al is shown to be composed, in time sequence...

  4. The Feynman-Dyson view

    International Nuclear Information System (INIS)

    Gill, Tepper L.

    2017-01-01

    This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics. (paper)

  5. The Feynman-Dyson view

    Science.gov (United States)

    Gill, Tepper L.

    2017-05-01

    This paper is a survey of our work on the mathematical foundations for the Feynman-Dyson program in quantum electrodynamics (QED). After a brief discussion of the history, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson’s second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman’s path integral, and to prove Dyson’s first conjecture that the divergences are in part due to a violation of Heisenberg’s uncertainly relations. As a by-product, we also prove Feynman’s conjecture about the relationship between the operator calculus and has path integral. Thus, providing the first rigorous justification for the Feynman formulation of quantum mechanics.

  6. Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method

    Science.gov (United States)

    Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo

    2012-01-01

    This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)

  7. Numerical Feynman integrals with physically inspired interpolation: Faster convergence and significant reduction of computational cost

    Directory of Open Access Journals (Sweden)

    Nikesh S. Dattani

    2012-03-01

    Full Text Available One of the most successful methods for calculating reduced density operator dynamics in open quantum systems, that can give numerically exact results, uses Feynman integrals. However, when simulating the dynamics for a given amount of time, the number of time steps that can realistically be used with this method is always limited, therefore one often obtains an approximation of the reduced density operator at a sparse grid of points in time. Instead of relying only on ad hoc interpolation methods (such as splines to estimate the system density operator in between these points, I propose a method that uses physical information to assist with this interpolation. This method is tested on a physically significant system, on which its use allows important qualitative features of the density operator dynamics to be captured with as little as two time steps in the Feynman integral. This method allows for an enormous reduction in the amount of memory and CPU time required for approximating density operator dynamics within a desired accuracy. Since this method does not change the way the Feynman integral itself is calculated, the value of the density operator approximation at the points in time used to discretize the Feynamn integral will be the same whether or not this method is used, but its approximation in between these points in time is considerably improved by this method. A list of ways in which this proposed method can be further improved is presented in the last section of the article.

  8. Integral Hellmann--Feynman analysis of nonisoelectronic processes and the determination of local ionization potentials

    International Nuclear Information System (INIS)

    Simons, G.

    1975-01-01

    The integral Hellmann--Feynmann theorem is extended to apply to nonisoelectronic processes. A local ionization potential formula is proposed, and test calculations on three different approximate helium wavefunctions are reported which suggest that it may be numerically superior to the standard difference of expectation values. Arguments for the physical utility of the new concept are presented, and an integral Hellmann--Feynman analysis of transition energies is begun

  9. The signed permutation group on Feynman graphs

    Energy Technology Data Exchange (ETDEWEB)

    Purkart, Julian, E-mail: purkart@physik.hu-berlin.de [Institute of Physics, Humboldt University, D-12489 Berlin (Germany)

    2016-08-15

    The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.

  10. Near threshold expansion of Feynman diagrams

    International Nuclear Information System (INIS)

    Mendels, E.

    2005-01-01

    The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an arbitrary number of internal lines and an arbitrary number of loops, in n dimensions and all masses may be different. The expansions are considered both below and above threshold. Rules, giving real and imaginary part, are derived. Unitarity of a sunset diagram with I internal lines is checked in a direct way by showing that its imaginary part is equal to the phase space integral of I particles

  11. Fuchsia. A tool for reducing differential equations for Feynman master integral to epsilon form

    Energy Technology Data Exchange (ETDEWEB)

    Gituliar, Oleksandr [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Magerya, Vitaly

    2017-01-15

    We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂{sub x}f(x,ε)=A(x,ε)f(x,ε) finds a basis transformation T(x,ε), i.e., f(x,ε)=T(x,ε)g(x,ε), such that the system turns into the epsilon form: ∂{sub x}g(x,ε)=εS(x)g(x,ε), where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ε. That makes the construction of the transformation T(x,ε) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals.

  12. Fuchsia. A tool for reducing differential equations for Feynman master integral to epsilon form

    International Nuclear Information System (INIS)

    Gituliar, Oleksandr; Magerya, Vitaly

    2017-01-01

    We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂ x f(x,ε)=A(x,ε)f(x,ε) finds a basis transformation T(x,ε), i.e., f(x,ε)=T(x,ε)g(x,ε), such that the system turns into the epsilon form: ∂ x g(x,ε)=εS(x)g(x,ε), where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ε. That makes the construction of the transformation T(x,ε) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals.

  13. Constructive Representation Theory for the Feynman Operator Calculus

    CERN Document Server

    Gill, T L

    2006-01-01

    In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of semigroup theory, including the Hille-Yosida theorem. As an application, we unify and extend the theory of time-dependent parabolic and hyperbolic evolution equations. We then develop a general perturbation theory and use it to prove that all theories generated by semigroups are asympotic in the operator-valued sense of Poincar e. This allows us to provide a general theory for the interaction representation of relativistic quantum theory. We then show that our theory can be reformulated as a physically motivated sum over paths, and use this version to extend the Feynman path integral to include more general interaction...

  14. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, J.; Radu, C.S.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Van Hoeij, M.; Imamoglu, E. [Florida State Univ., Tallahassee, FL (United States). Dept. of Mathematics; Raab, C.G. [Linz Univ. (Austria). Inst. for Algebra

    2017-05-15

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as {sub 2}F{sub 1} Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ{sub i} functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η{sup κ}(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  15. Iterated elliptic and hypergeometric integrals for Feynman diagrams

    International Nuclear Information System (INIS)

    Ablinger, J.; Radu, C.S.; Schneider, C.; Bluemlein, J.; Freitas, A. de; Van Hoeij, M.; Imamoglu, E.; Raab, C.G.

    2017-05-01

    We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as _2F_1 Gauss hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's θ_i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η"κ(τ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

  16. A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

    International Nuclear Information System (INIS)

    Motoki, S; Ishikawa, T; Yuasa, F; Daisaka, H; Nakasato, N; Fukushige, T; Kawai, A; Makino, J

    2015-01-01

    Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagrams with multi-loop integrals which may require multi-precision calculation. We developed a dedicated accelerator system for multiprecision calculations (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision. (paper)

  17. New results for algebraic tensor reduction of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center

    2012-02-15

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  18. New results for algebraic tensor reduction of Feynman integrals

    International Nuclear Information System (INIS)

    Fleischer, Jochem; Yundin, Valery

    2012-02-01

    We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)

  19. Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace

    Science.gov (United States)

    Hartung, Tobias

    2017-12-01

    A fully regulated definition of Feynman's path integral is presented here. The proposed re-formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined. In particular, it is consistent with respect to lattice formulations and Wick rotations, i.e., it can be used in Euclidean and Minkowski space-time. The path integral regularization is introduced through the generalized Kontsevich-Vishik trace, that is, the extension of the classical trace to Fourier integral operators. Physically, we are replacing the time-evolution semi-group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of C . The regularized path integral is, thus, defined through analytic continuation. This regularization can be performed by means of stationary phase approximation or computed analytically depending only on the Hamiltonian and the observable (i.e., known a priori). In either case, the computational effort to evaluate path integrals or expectations of observables reduces to the evaluation of integrals over spheres. Furthermore, computations can be performed directly in the continuum and applications (analytic computations and their implementations) to a number of models including the non-trivial cases of the massive Schwinger model and a φ4 theory.

  20. Mellin-Barnes meets Method of Brackets: a novel approach to Mellin-Barnes representations of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Prausa, Mario [RWTH Aachen University, Institute for Theoretical Particle Physics and Cosmology, Aachen (Germany)

    2017-09-15

    In this paper, we present a new approach to the construction of Mellin-Barnes representations for Feynman integrals inspired by the Method of Brackets. The novel technique is helpful to lower the dimensionality of Mellin-Barnes representations in complicated cases, some examples are given. (orig.)

  1. Feynman versus Bakamjian-Thomas in light-front dynamics

    International Nuclear Information System (INIS)

    Araujo, W.R.B. de; Beyer, M.; Weber, H.J.; Frederico, T.

    1999-01-01

    We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light-front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated. (author)

  2. Factorization in QCD in Feynman gauge

    International Nuclear Information System (INIS)

    Tucci, R.R.

    1985-01-01

    We present a mass divergence power counting technique for QCD in the Feynman gauge. For the process γ/sup */ → qq, we find the leading regions of integration and show that single diagrams are at worst logarithmically divergent. Using the Weyl representation facilities the γ matrix manipulations necessary for power counting and adds much physical insight. We prove Ward type identities which are needed in the proof of factorization of the Drill Yan process. Previous treatments prove them only for an axial gauge, and the proofs are diagrammatic in nature. We, on the other hand, establish the identities for the Feynman gauge and through symmetry considerations at the Lagrangian level. The strategy is to first derive exact results in a background field gauge and then to show that to leading order in the mass divergences the background field gauge results can be used in the Feynman gauge

  3. Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

    Science.gov (United States)

    Gituliar, Oleksandr; Magerya, Vitaly

    2017-10-01

    We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂x J(x , ɛ) = A(x , ɛ) J(x , ɛ) finds a basis transformation T(x , ɛ) , i.e., J(x , ɛ) = T(x , ɛ) J‧(x , ɛ) , such that the system turns into the epsilon form : ∂xJ‧(x , ɛ) = ɛ S(x) J‧(x , ɛ) , where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ɛ. That makes the construction of the transformation T(x , ɛ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program Files doi:http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language:Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ɛ-series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization. During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ɛ. Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations. Additional comments

  4. Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0

    International Nuclear Information System (INIS)

    Dubovyk, Ievgen; Gluza, Janusz; Riemann, Tord

    2016-04-01

    We introduce the Mellin-Barnes representation of general Feynman integrals and discuss their evaluation. The Mathematica package AMBRE has been recently extended in order to cover consistently non-planar Feynman integrals with two loops. Prospects for the near future are outlined. This write-up is an introduction to new results which have also been presented elsewhere.

  5. A convergence theorem for asymptotic expansions of Feynman amplitudes

    International Nuclear Information System (INIS)

    Mabouisson, A.P.C.

    1999-06-01

    The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to ∞, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)

  6. Introduction to Feynman diagrams

    CERN Document Server

    Bilenky, Samoil Mikhelevich

    1974-01-01

    Introduction to Feynman Diagrams provides Feynman diagram techniques and methods for calculating quantities measured experimentally. The book discusses topics Feynman diagrams intended for experimental physicists. Topics presented include methods for calculating the matrix elements (by perturbation theory) and the basic rules for constructing Feynman diagrams; techniques for calculating cross sections and polarizations; processes in which both leptons and hadrons take part; and the electromagnetic and weak form factors of nucleons. Experimental physicists and graduate students of physics will

  7. Acceleration of Feynman loop integrals in high-energy physics on many core GPUs

    International Nuclear Information System (INIS)

    Yuasa, F; Ishikawa, T; Hamaguchi, N; Koike, T; Nakasato, N

    2013-01-01

    The current and future colliders in high-energy physics require theorists to carry out a large scale computation for a precise comparison between experimental results and theoretical ones. In a perturbative approach several methods to evaluate Feynman loop integrals which appear in the theoretical calculation of cross-sections are well established in the one-loop level, however, more studies are necessary for higher-order levels. Direct Computation Method (DCM) is developed to evaluate multi-loop integrals. DCM is based on a combination of multidimensional numerical integration and extrapolation on a sequence of integrals. It is a fully numerical method and is applicable to a wide class of integrals with various physics parameters. The computation time depends on physics parameters and the topology of loop diagrams and it becomes longer for the two-loop integrals. In this paper we present our approach to the acceleration of the two-loop integrals by DCM on multiple GPU boards

  8. Finding new relationships between hypergeometric functions by evaluating Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Kniehl, Bernd A. [Santa Barbara Univ., CA (United States). Kavli Inst. for Theoretical Physics; Tarasov, Oleg V. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2011-08-15

    Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and arbitrary powers of propagators is derived in terms of only one Appell hypergeometric function F{sub 1}. From the comparison of this expression with a previously known one, a new relation between the Appell functions F{sub 1} and F{sub 4} is found. By comparing this new expression for the case of equal masses with another known result, a new formula for reducing the F{sub 1} function with particular arguments to the hypergeometric function {sub 3}F{sub 2} is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F{sub 1} functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F{sub 1} function is found by analysing the imaginary part of the two-loop self-energy integral on the cut. An explicit formula relating the F{sub 1} function and the Gaussian hypergeometric function {sub 2}F{sub 1} whose argument is the ratio of polynomials of degree six is presented. (orig.)

  9. Transforming differential equations of multi-loop Feynman integrals into canonical form

    Energy Technology Data Exchange (ETDEWEB)

    Meyer, Christoph [Institut für Physik, Humboldt-Universität zu Berlin,12489 Berlin (Germany)

    2017-04-03

    The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.

  10. Transforming differential equations of multi-loop Feynman integrals into canonical form

    Science.gov (United States)

    Meyer, Christoph

    2017-04-01

    The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.

  11. Transforming differential equations of multi-loop Feynman integrals into canonical form

    International Nuclear Information System (INIS)

    Meyer, Christoph

    2017-01-01

    The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.

  12. Quantum Man: Richard Feynman's Life in Science

    CERN Document Server

    CERN. Geneva

    2011-01-01

    It took a man who was willing to break all the rules to tame a theory that breaks all the rules. This talk will be based on my new book Quantum Man: Richard Feynman's life in science. I will try and present a scientific overview of the contributions of Richard Feynman, as seen through the arc of his fascinating life. From Quantum Mechanics to Antiparticles, from Rio de Janeiro to Los Alamos, a whirlwind tour will provide insights into the character, life and accomplishments of one of the 20th centuries most important scientists, and provide an object lesson in scientific integrity.

  13. Parallel Implementation of Numerical Solution of Few-Body Problem Using Feynman's Continual Integrals

    Science.gov (United States)

    Naumenko, Mikhail; Samarin, Viacheslav

    2018-02-01

    Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman's continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He) and nuclei described as consisting of clusters and nucleons (e.g., 6He). The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.

  14. Numerical evaluation of Feynman loop integrals by reduction to tree graphs

    International Nuclear Information System (INIS)

    Kleinschmidt, T.

    2007-12-01

    We present a method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. This states that loop graphs can be expressed as a sum of tree graphs with additional external on-shell particles. The original loop integral is replaced by a phase space integration over the additional particles. In cross section calculations and for event generation, this phase space can be sampled simultaneously with the phase space of the original external particles. Since very sophisticated matrix element generators for tree graph amplitudes exist and phase space integrations are generically well understood, this method is suited for a future implementation in a fully automated Monte Carlo event generator. A scheme for renormalization and regularization is presented. We show the construction of subtraction graphs which cancel ultraviolet divergences and present a method to cancel internal on-shell singularities. Real emission graphs can be naturally included in the phase space integral of the additional on-shell particles to cancel infrared divergences. As a proof of concept, we apply this method to NLO Bhabha scattering in QED. Cross sections are calculated and are in agreement with results from conventional methods. We also construct a Monte Carlo event generator and present results. (orig.)

  15. Numerical evaluation of Feynman loop integrals by reduction to tree graphs

    Energy Technology Data Exchange (ETDEWEB)

    Kleinschmidt, T.

    2007-12-15

    We present a method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. This states that loop graphs can be expressed as a sum of tree graphs with additional external on-shell particles. The original loop integral is replaced by a phase space integration over the additional particles. In cross section calculations and for event generation, this phase space can be sampled simultaneously with the phase space of the original external particles. Since very sophisticated matrix element generators for tree graph amplitudes exist and phase space integrations are generically well understood, this method is suited for a future implementation in a fully automated Monte Carlo event generator. A scheme for renormalization and regularization is presented. We show the construction of subtraction graphs which cancel ultraviolet divergences and present a method to cancel internal on-shell singularities. Real emission graphs can be naturally included in the phase space integral of the additional on-shell particles to cancel infrared divergences. As a proof of concept, we apply this method to NLO Bhabha scattering in QED. Cross sections are calculated and are in agreement with results from conventional methods. We also construct a Monte Carlo event generator and present results. (orig.)

  16. On the maximal cut of Feynman integrals and the solution of their differential equations

    Directory of Open Access Journals (Sweden)

    Amedeo Primo

    2017-03-01

    Full Text Available The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ=(4−d/2, where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.

  17. Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

    Science.gov (United States)

    Field, J. H.

    2011-01-01

    It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

  18. Feynman and physics. Life and research of an exceptional man; Feynman und die Physik. Leben und Forschung eines aussergewoehnlichen Menschen

    Energy Technology Data Exchange (ETDEWEB)

    Resag, Joerg

    2018-04-01

    The life of Feynman is described together with his work on path integrals, quantum electrodynmaics, helium at low temperatures, the weak interaction, the quark model, and computer-calculation methods, and his contribution to the Manhattan project. (HSI)

  19. Differential reduction of generalized hypergeometric functions from Feynman diagrams. One-variable case

    Energy Technology Data Exchange (ETDEWEB)

    Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik

    2010-03-15

    The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is discussed in the context of evaluating Feynman diagrams. Where this is possible, we compare our results with those obtained using standard techniques. It is shown that the criterion of reducibility of multiloop Feynman integrals can be reformulated in terms of the criterion of reducibility of hypergeometric functions. The relation between the numbers of master integrals obtained by differential reduction and integration by parts is discussed. (orig.)

  20. Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

    International Nuclear Information System (INIS)

    Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

    2012-05-01

    We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.

  1. Professor Richard Feynman colloquium

    CERN Multimedia

    1965-01-01

    Richard P. Feynman received the Nobel Prize for physics in 1965. Following the ceremony in Stockholm, Feynman gave the colloquium "Development of the space-time view of quantum electrodynamics" at CERN on 17th December.

  2. Feynman Lectures on Computation

    CERN Document Server

    Feynman, Richard Phillips; Allen, Robin W

    1999-01-01

    "When, in 1984-86, Richard P. Feynman gave his famous course on computation at the California Institute of Technology, he asked Tony Hey to adapt his lecture notes into a book. Although led by Feynman,"

  3. Detailed balance of the Feynman micromotor

    Science.gov (United States)

    Abbott, Derek; Davis, Bruce R.; Parrondo, Juan M. R.

    1999-09-01

    One existing implication of micromotors is that they can be powered by rectifying non-equilibrium thermal fluctuations or mechanical vibrations via the so-called Feynman- micromotor. An example of mechanical rectification is found in the batteryless wristwatch. The original concept was described in as early as 1912 by Smoluchowski and was later revisited in 1963 by Feynman, in the context of rectifying thermal fluctuations to obtain useful motion. It has been shown that, although rectification is impossible at equilibrium, it is possible for the Feynman-micromotor to perform work under non-equilibrium conditions. These concepts can now be realized by MEMS technology and may have exciting implications in biomedicine - where the Feynman- micromotor can be used to power a smart pill, for example. Previously, Feynman's analysis of the motor's efficiency has been shown to be flawed by Parrondo and Espanol. We now show there are further problems in Feynman's treatment of detailed balance. In order to design and understand this device correctly, the equations of detailed balance must be found. Feynman's approach was to use probabilities based on energies and we show that this is problematic. In this paper, we demonstrate corrected equations using level crossing probabilities instead. A potential application of the Feynman-micromotor is a batteryless nanopump that consists of a small MEMS chip that adheres to the skin of a patient and dispense nanoliter quantities of medication. Either mechanical or thermal rectification via a Feynman- micromotor, as the power source, is open for possible investigation.

  4. Perturbation theory via Feynman diagrams in classical mechanics

    OpenAIRE

    Penco, R.; Mauro, D.

    2006-01-01

    In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

  5. Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    1978-01-01

    An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer

  6. Feynman's operational calculus and beyond noncommutativity and time-ordering

    CERN Document Server

    Johnson, George W; Nielsen, Lance

    2015-01-01

    This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...

  7. Feynman diagrams without Feynman parameters

    International Nuclear Information System (INIS)

    Mendels, E.

    1978-01-01

    Dimensionally regularized Feynman diagrams are represented by means of products of k-functions. The infinite part of these diagrams is found very easily, also if they are overlapping, and the separation of the several kinds of divergences comes out quite naturally. Ward identities are proven in a transparent way. Series expansions in terms of the external momenta and their inner products are possible

  8. Feynman Lectures on Gravitation

    International Nuclear Information System (INIS)

    Borcherds, P

    2003-01-01

    In the early 1960s Feynman lectured to physics undergraduates and, with the assistance of his colleagues Leighton and Sands, produced the three-volume classic Feynman Lectures in Physics. These lectures were delivered in the mornings. In the afternoons Feynman was giving postgraduate lectures on gravitation. This book is based on notes compiled by two students on that course: Morinigo and Wagner. Their notes were checked and approved by Feynman and were available at Caltech. They have now been edited by Brian Hatfield and made more widely available. The book has a substantial preface by John Preskill and Kip Thorne, and an introduction entitled 'Quantum Gravity' by Brian Hatfield. You should read these before going on to the lectures themselves. Preskill and Thorne identify three categories of potential readers of this book. 1. Those with a postgraduate training in theoretical physics. 2. 'Readers with a solid undergraduate training in physics'. 3. 'Admirers of Feynman who do not have a strong physics background'. The title of the book is perhaps misleading: readers in category 2 who think that this book is an extension of the Feynman Lectures in Physics may be disappointed. It is not: it is a book aimed mainly at those in category 1. If you want to get to grips with gravitation (and general relativity) then you need to read an introductory text first e.g. General Relativity by I R Kenyon (Oxford: Oxford University Press) or A Unified Grand Tour of Theoretical Physics by Ian D Lawrie (Bristol: IoP). But there is no Royal Road. As pointed out in the preface and in the introduction, the book represents Feynman's thinking about gravitation some 40 years ago: the lecture course was part of his attempts to understand the subject himself, and for readers in all three categories it is this that makes the book one of interest: the opportunity to observe how a great physicist attempts to tackle some of the hardest challenges of physics. However, the book was written 40

  9. Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

    Energy Technology Data Exchange (ETDEWEB)

    Perkins, R. J., E-mail: rperkins@pppl.gov; Bellan, P. M. [Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125 (United States)

    2015-02-15

    Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle in a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.

  10. Feynman and physics. Life and research of an exceptional man

    International Nuclear Information System (INIS)

    Resag, Joerg

    2018-01-01

    The life of Feynman is described together with his work on path integrals, quantum electrodynmaics, helium at low temperatures, the weak interaction, the quark model, and computer-calculation methods, and his contribution to the Manhattan project. (HSI)

  11. FeynRules - Feynman rules made easy

    OpenAIRE

    Christensen, Neil D.; Duhr, Claude

    2008-01-01

    In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g. particle content, parameters and Lagrangian), FeynRules derives the Feynman rules and stores them in a generic form suitable for translation to any Feynman diagram calculation program. The model can then be translated to the format specific to a particular Feynman diagram calculator via F...

  12. A new approach to the Taylor expansion of multiloop Feynman diagrams

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    1996-01-01

    We present a new method for the Taylor expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the small momentum expansion of an arbitrary diagram. The method is applicable for the expansion with respect to all or a subset of external momenta. The coefficients of the expansion are obtained by applying a differential operator to a given integral with shifted value of the space-time dimension d and the expansion momenta set equal to zero. Integrals with changed d are evaluated by using the generalized recurrence relations recently proposed [O.V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, preprint DESY 96-068, JINR E2-96-62 (hep-th/9606018), to be published in Phys. Rev. D 54, No. 10 (1996)]. We show how the method works for one- and two-loop integrals. It is also illustrated that our method is simpler and more efficient than others. (orig.)

  13. The R{sup ∗}-operation for Feynman graphs with generic numerators

    Energy Technology Data Exchange (ETDEWEB)

    Herzog, Franz [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Ruijl, Ben [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Leiden University,Niels Bohrweg 1, 2333 CA Leiden (Netherlands)

    2017-05-08

    The R{sup ∗}-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R{sup ∗}-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional ϕ{sup 3} theory.

  14. FF. A package to evaluate one-loop Feynman diagrams

    International Nuclear Information System (INIS)

    Oldenborgh, G.J. van

    1990-09-01

    A short description and a user's guide of the FF package are given. This package contains routines to evaluate numerically the scalar one-loop integrals occurring in the evaluation in one-loop Feynman diagrams. The algorithms chosen are numerically stable over most parameter space. (author). 5 refs.; 1 tab

  15. Richard Feynman Quarks, Bombs, and Bongos

    CERN Document Server

    Henderson, Harry

    2010-01-01

    Described by his peers as the "finest physicist of his generation," Richard Feynman defied scientist stereotypes. This brash New York-born American physicist startled the more conservative giants of European physics with his endless ability to improvise. Indeed, later in life, Feynman became an accomplished bongo player. Feynman's legacy to physics was his ability to simplify complex equations and clarify fundamental principles through the use of graphs. He developed the theory of quantum electrodynamics, which illustrates the behavior of electrically charged particles, such as elect

  16. Huygens-Feynman-Fresnel principle as the basis of applied optics.

    Science.gov (United States)

    Gitin, Andrey V

    2013-11-01

    The main relationships of wave optics are derived from a combination of the Huygens-Fresnel principle and the Feynman integral over all paths. The stationary-phase approximation of the wave relations gives the correspondent relations from the point of view of geometrical optics.

  17. Path integral formulation and Feynman rules for phylogenetic branching models

    Energy Technology Data Exchange (ETDEWEB)

    Jarvis, P D; Bashford, J D; Sumner, J G [School of Mathematics and Physics, University of Tasmania, GPO Box 252C, 7001 Hobart, TAS (Australia)

    2005-11-04

    A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance.

  18. Path integral formulation and Feynman rules for phylogenetic branching models

    International Nuclear Information System (INIS)

    Jarvis, P D; Bashford, J D; Sumner, J G

    2005-01-01

    A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance

  19. A modern theory of random variation with applications in stochastic calculus, financial mathematics, and Feynman integration

    CERN Document Server

    Muldowney, Patrick

    2012-01-01

    A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...

  20. Analytic continuation of dual Feynman amplitudes

    International Nuclear Information System (INIS)

    Bleher, P.M.

    1981-01-01

    A notion of dual Feynman amplitude is introduced and a theorem on the existence of analytic continuation of this amplitude from the convergence domain to the whole complex is proved. The case under consideration corresponds to massless power propagators and the analytic continuation is constructed on the propagators powers. Analytic continuation poles and singular set of external impulses are found explicitly. The proof of the theorem on the existence of analytic continuation is based on the introduction of α-representation for dual Feynman amplitudes. In proving, the so-called ''trees formula'' and ''trees-with-cycles formula'' are established that are dual by formulation to the trees and 2-trees formulae for usual Feynman amplitudes. (Auth.)

  1. Automated generation of lattice QCD Feynman rules

    Energy Technology Data Exchange (ETDEWEB)

    Hart, A.; Mueller, E.H. [Edinburgh Univ. (United Kingdom). SUPA School of Physics and Astronomy; von Hippel, G.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Horgan, R.R. [Cambridge Univ. (United Kingdom). DAMTP, CMS

    2009-04-15

    The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)

  2. Automated generation of lattice QCD Feynman rules

    International Nuclear Information System (INIS)

    Hart, A.; Mueller, E.H.; Horgan, R.R.

    2009-04-01

    The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)

  3. The Feynman integrand as a white noise distribution beyond perturbation theory

    International Nuclear Information System (INIS)

    Grothaus, Martin; Vogel, Anna

    2008-01-01

    In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time-dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory

  4. Feynman diagram drawing made easy

    International Nuclear Information System (INIS)

    Baillargeon, M.

    1997-01-01

    We present a drawing package optimised for Feynman diagrams. These can be constructed interactively with a mouse-driven graphical interface or from a script file, more suitable to work with a diagram generator. It provides most features encountered in Feynman diagrams and allows to modify every part of a diagram after its creation. Special attention has been paid to obtain a high quality printout as easily as possible. This package is written in Tcl/Tk and in C. (orig.)

  5. Beyond Feynman Diagrams (1/3)

    CERN Multimedia

    CERN. Geneva

    2013-01-01

    For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past few years, alternative methods that go beyond ...

  6. The diamond rule for multi-loop Feynman diagrams

    International Nuclear Information System (INIS)

    Ruijl, B.; Ueda, T.; Vermaseren, J.A.M.

    2015-01-01

    An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to achieve simple reduction schemes. In this work we introduce an extensible, multi-loop version of the triangle rule, which we refer to as the diamond rule. Such a structure appears frequently in higher-loop calculations. We derive an explicit solution for the recursion, which prevents spurious poles in intermediate steps of the computations. Applications for massless propagator type diagrams at three, four, and five loops are discussed

  7. (U) Feynman-Y calculations using PARTISN

    Energy Technology Data Exchange (ETDEWEB)

    Favorite, Jeffrey A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-08-31

    A prescription for computing the Feynman Y as a function of coincidence gate width using a deterministic multigroup neutron transport code has been published and the results compared favorably with measurements of the BeRP ball. In this paper, we report on our project to implement the method and reproduce the results. There are several clarifications and corrections of the published prescription. We show results using two multigroup cross section libraries compared with measurements and with Monte Carlo results. Deterministic simulations of the mean count rates compare very favorably with previously published Monte Carlo results, and deterministic simulations of the Feynman Y asymptote compare somewhat favorably. In Feynman beta plots, the deterministic simulations reached the asymptotic value much sooner than did a fit to the measured data.

  8. Spin wave Feynman diagram vertex computation package

    Science.gov (United States)

    Price, Alexander; Javernick, Philip; Datta, Trinanjan

    Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.

  9. Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism

    Science.gov (United States)

    Aurell, Erik

    2018-04-01

    The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere S^2 as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators \\hat{S}_z . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.

  10. Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism

    Science.gov (United States)

    Aurell, Erik

    2018-06-01

    The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere S^2 as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators \\hat{S}_z. The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.

  11. A Feynman graph selection tool in GRACE system

    International Nuclear Information System (INIS)

    Yuasa, Fukuko; Ishikawa, Tadashi; Kaneko, Toshiaki

    2001-01-01

    We present a Feynman graph selection tool grcsel, which is an interpreter written in C language. In the framework of GRACE, it enables us to get a subset of Feynman graphs according to given conditions

  12. Application of difference filter to Feynman-α analysis

    International Nuclear Information System (INIS)

    Mouri, Tomoaki; Ohtani, Nobuo

    1997-11-01

    The Feynman-α method has been developed for monitoring sub-criticality in nuclear fuel facilities. It is difficult to apply the Feynman-α method which estimates statistical variation of the number of neutron counts per unit time, to the system in transient condition such that the averaged neutron flux varies with time. In the application of Feynman-α method to such system, it is suggested to remove the averaged variation of neutron flux from neutron count data by the use of the difference filter. In this study, we applied the difference filter to reactor noise data at sub-criticality near to criticality, where the prompt decay constant was difficult to estimate due to the large effect of delayed neutron. With the difference filter, accurate prompt decay constants for effective multiplication factors from 0.999 to 0.994 were obtained by Feynman-α method. It was cleared that the difference filter is effective to estimate accurate prompt decay constant, so that there is the prospect to be able to apply Feynman-α method having the difference filter to the system in the transient condition. (author)

  13. Feynman diagrams coupled to three-dimensional quantum gravity

    International Nuclear Information System (INIS)

    Barrett, John W

    2006-01-01

    A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero

  14. Appell functions and the scalar one-loop three-point integrals in Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Cabral-Rosetti, L G [Departamento de Posgrado, Centro Interdisciplinario de Investigacion y Docencia en Educacion Tecnica (CIIDET), Av. Universidad 282 Pte., Col. Centro, A. Postal 752, C.P. 76000, Santiago de Queretaro, Qro. (Mexico); Sanchis-Lozano, M A [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, 46100 Burjassot, Valencia (Spain)

    2006-05-15

    The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.

  15. Feynman propagator for a particle with arbitrary spin

    International Nuclear Information System (INIS)

    Huang Shi-Zhong; Zhang Peng-Fei; Ruan Tu-Nan; Zhu Yu-Can; Zheng Zhi-Peng

    2005-01-01

    Based on the solution to the Rarita-Schwinger equations, a direct derivation of the projection operator and propagator for a particle with arbitrary spin is worked out. The projection operator constructed by Behrends and Fronsdal is re-deduced and confirmed, and simplified in the case of half-integral spin; the general commutation rules and Feynman propagator for a free particle of any spin are derived, and explicit expressions for the propagators for spins 3/2, 2, 5/2, 3, 7/2, 4 are provided. (orig.)

  16. Counting the number of Feynman graphs in QCD

    Science.gov (United States)

    Kaneko, T.

    2018-05-01

    Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

  17. Richard Phillips Feynman

    Indian Academy of Sciences (India)

    ARTICLE-IN-A-BOX. 797. RESONANCE │ September 2011. The war years interrupted the efforts of both Feynman and Schwinger to tackle the divergence problems in quantum electrodynamics, another of Dirac's pioneering creations from 1927. In 1965 the Physics Nobel Prize was shared by the two of them and Sin-Ichiro ...

  18. The Feynman fluid analogy in e+e- annihilation

    International Nuclear Information System (INIS)

    Hegyi, S.; Krasznovszky, S.

    1990-07-01

    An analysis of the charged particle multiplicity distributions observed in e + e - annihilation is given using the generalized Feynman fluid analogy of multiparticle production. Only the two-and three-particle integrated correlation functions are included into the scheme. It is shown that the model correctly describes the available experimental data from the TASSO and HRS collaborations. Some properties of the fluid of the analogy are computed and a prediction is made for the multiplicity distribution at √s = 91 GeV. (author) 19 refs.; 5 figs.; 1 tab

  19. One loop integrals reduction

    International Nuclear Information System (INIS)

    Sun Yi; Chang Haoran

    2012-01-01

    By further examining the symmetry of external momenta and masses in Feynman integrals, we fulfilled the method proposed by Battistel and Dallabona, and showed that recursion relations in this method can be applied to simplify Feynman integrals directly. (authors)

  20. Richard Phillips Feynman

    Indian Academy of Sciences (India)

    While the two relativity theories were largely the creation of Albert Einstein, the quantum ... of what may lie in store for anyone who dares to follow the beat of a different drum. ... saw Feynman's exceptional talents and in a special lecture explained to him the beautiful principle ... The Character of Physical Law – 1965. c).

  1. Foundations for relativistic quantum theory. I. Feynman's operator calculus and the Dyson conjectures

    International Nuclear Information System (INIS)

    Gill, Tepper L.; Zachary, W.W.

    2002-01-01

    In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

  2. To Have Been a Student of Richard Feynman

    Indian Academy of Sciences (India)

    Excerpt from Most of the Good Stuff: Memories of Richard Feynman, 1993, ... of Feynman, but while it inspired us to try for originality after we left Cornell, it also lowered our productivity to a point that at times was dangerous to our academic careers. In truth .... (However, my actual thesis topic turned out to be a different one.).

  3. Feynman rules for fermion-number-violating interactions

    International Nuclear Information System (INIS)

    Denner, A.; Eck, H.; Hahn, O.; Kueblbeck, J.

    1992-01-01

    We present simple algorithmic Feynman rules for fermion-number-violating interactions. They do not involve explicit charge-conjugation matrices and resemble closely the familiar rules for Dirac fermions. We insist on a fermion flow through the graphs along fermion lines and get the correct relative signs between different interfering Feynman graphs as in the case of Dirac fermions. We only need the familiar Dirac propagator and fewer vertices than in the usual treatment of fermion-number-violating interactions. (orig.)

  4. The Hellman-Feynman theorem at finite temperature

    International Nuclear Information System (INIS)

    Cabrera, A.; Calles, A.

    1990-01-01

    The possibility of a kind of Hellman-Feynman theorem at finite temperature is discussed. Using the cannonical ensembles, the derivative of the internal energy is obtained when it depends explicitly on a parameter. It is found that under the low temperature regime the derivative of the energy can be obtained as the statistical average of the derivative of the hamiltonian operator. The result allows to speak of the existence of the Hellman-Feynman theorem at finite temperatures (Author)

  5. Feynman's thesis: A new approach to quantum theory

    International Nuclear Information System (INIS)

    Das, Ashok

    2007-01-01

    It is not usual for someone to write a book on someone else's Ph.D. thesis, but then Feynman was not a usual physicist. He was without doubt one of the most original physicists of the twentieth century, who has strongly influenced the developments in quantum field theory through his many ingenious contributions. Path integral approach to quantum theories is one such contribution which pervades almost all areas of physics. What is astonishing is that he developed this idea as a graduate student for his Ph.D. thesis which has been printed, for the first time, in the present book along with two other related articles. The early developments in quantum theory, by Heisenberg and Schroedinger, were based on the Hamiltonian formulation, where one starts with the Hamiltonian description of a classical system and then promotes the classical observables to noncommuting quantum operators. However, Dirac had already stressed in an article in 1932 (this article is also reproduced in the present book) that the Lagrangian is more fundamental than the Hamiltonian, at least from the point of view of relativistic invariance and he wondered how the Lagrangian may enter into the quantum description. He had developed this idea through his 'transformation matrix' theory and had even hinted on how the action of the classical theory may enter such a description. However, although the brief paper by Dirac contained the basic essential ideas, it did not fully develop the idea of a Lagrangian description in detail in the functional language. Feynman, on the other hand, was interested in the electromagnetic interactions of the electron from a completely different point of view rooted in a theory involving action-at-a-distance. His theory (along with John Wheeler) did not have a Hamiltonian description and, in order to quantize such a theory, he needed an alternative formulation of quantum mechanics. When the article by Dirac was brought to his attention, he immediately realized what he was

  6. A LaTeX graphics routine for drawing Feynman diagrams

    International Nuclear Information System (INIS)

    Levine, M.J.S.

    1990-01-01

    FEYNMAN is a LaTeX macropackage which allows the user to construct a versatile range of Feynman diagrams within the text of a document. Diagrams of publication quality may be drawn with relative ease and rapidity. (orig.)

  7. Electrodynamic metaphors: communicating particle physics with Feynman diagrams

    Directory of Open Access Journals (Sweden)

    Pietroni Massimo

    2002-03-01

    Full Text Available The aim of this project is to communicate the basic laws of particle physics with Feynman diagrams - visual tools which represent elementary particle processes. They were originally developed as a code to be used by physicists and are still used today for calculations and elaborations of theoretical nature. The technical and mathematical rules of Feynman diagrams are obviously the exclusive concern of physicists, but on a pictorial level they can help to popularize many concepts, ranging from matter and the antimatter; the creation, destruction and transformation of particles; the role of ‘virtual’ particles in interactions; the conservation laws, symmetries, etc. Unlike the metaphors often used to describe the microcosm, these graphic representations provide an unequivocal translation of the physical content of the underlying quantum theory. As such they are perfect metaphors, not misleading constructions. A brief introduction on Feynman diagrams will be followed by the practical realization of this project, which will be carried out with the help of an experiment based on three-dimensional manipulable objects. The Feynman rules are expressed in terms of mechanical constraints on the possible conjuctions among the various elements of the experiment. The final part of the project will present the results of this experiment, which has been conducted among high-school students.

  8. Bootstrap Sequential Determination of the Co-integration Rank in VAR Models

    DEFF Research Database (Denmark)

    Guiseppe, Cavaliere; Rahbæk, Anders; Taylor, A.M. Robert

    with empirical rejection frequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the co-integrating rank based on these bootstrap tests need to be consistent, in the sense...... in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlo simulations show the proposed procedure performs well in practice....

  9. Coupled oscillators and Feynman's three papers

    International Nuclear Information System (INIS)

    Kim, Y S

    2007-01-01

    According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators

  10. Feynman propagator for spin foam quantum gravity.

    Science.gov (United States)

    Oriti, Daniele

    2005-03-25

    We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".

  11. A New Comment on Dyson's Exposition of Feynman's Proof of Maxwell Equations

    International Nuclear Information System (INIS)

    Pombo, Claudia

    2009-01-01

    A paper by Dyson, published nearly two decades ago, describing Feynman's proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman's derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton's physics is not a starting point in Feynman's derivation, neither is quantum physics involved in it, but the foundations of relativity only.

  12. Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral

    International Nuclear Information System (INIS)

    Lin, T.L.; Wang, R.; Bi, W.P.; El Kaabouchi, A.; Pujos, C.; Calvayrac, F.; Wang, Q.A.

    2013-01-01

    We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, divided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems

  13. Feynman variance-to-mean method

    International Nuclear Information System (INIS)

    Dowdy, E.J.; Hansen, G.E.; Robba, A.A.

    1985-01-01

    The Feynman and other fluctuation techniques have been shown to be useful for determining the multiplication of subcritical systems. The moments of the counting distribution from neutron detectors is analyzed to yield the multiplication value. The authors present the methodology and some selected applications and results and comparisons with Monte Carlo calculations

  14. Automatically generating Feynman rules for improved lattice field theories

    International Nuclear Information System (INIS)

    Hart, A.; Hippel, G.M. von; Horgan, R.R.; Storoni, L.C.

    2005-01-01

    Deriving the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially when improvement terms are present. This physically important task is, however, suitable for automation. We describe a flexible algorithm for generating Feynman rules for a wide range of lattice field theories including gluons, relativistic fermions and heavy quarks. We also present an efficient implementation of this in a freely available, multi-platform programming language (PYTHON), optimised to deal with a wide class of lattice field theories

  15. Basics of introduction to Feynman diagrams and electroweak interactions physics

    International Nuclear Information System (INIS)

    Bilenky, S.M.; Mikhov, S.G.

    1994-01-01

    The Feynman diagrams are the main computational method for the evaluation of the matrix elements of different processes. Although it is a perturbative method, its significance is not restricted to perturbation theory only. In this book, the elements of quantum field theory, the Feynman diagram method, the theory of electroweak interactions and other topics are discussed. A number of classical weak and electroweak processes are considered in details. This involves, first of all, the construction of the matrix elements of the process using both the Feynman diagram method (when perturbation theory can be applied) and the invariance principles (when perturbation theory fails). Then the cross sections and the decay probabilities are computed. The text is providing widely used computational techniques and some experimental data. (A.B.). 32 refs., 7 appendix

  16. A multi-region multi-energy formalism for the Feynman-alpha formulas

    International Nuclear Information System (INIS)

    Malinovitch, T.; Dubi, C.

    2015-01-01

    Highlights: • A formalism of N regions and M groups for the Feynman-α method is introduced. • Using a space-energy cell notation the expressions are simplified significantly. • A simple way to incorporate the detectors in the system is used. • The results have been verified by a Monte Carlo simulation in a two-region case. - Abstract: The stochastic transport equation, describing the dynamics in time of the neutron population in a nuclear system, is used to gain expressions for the higher moments of the neutron population in a sub-critical system. Such expressions are the bone structure of the so called Feynman-α method to analyze noise experiments, aimed to determine the reactivity of sub-critical systems. In the present study, a general formalism for the stochastic transport equation in an N regions system, under the M energy groups approximation will be introduced. In particular, expressions for the Feynman variance to mean (or the Feynman-Y function) under the above mentioned restriction will be sought by using the steady state mode of the solution

  17. Extension of a theory of Feynman

    International Nuclear Information System (INIS)

    Blaquiere, Augustin

    1979-01-01

    We propose a relativistic extension of a method through which Feynman derives the Schroedinger equation. The equation of Klein-Gordon for a charged particle in a magnetic field is obtained. Some connections with the nonrelativistic and the classical approximations are discussed [fr

  18. Automation of Feynman diagram evaluations

    International Nuclear Information System (INIS)

    Tentyukov, M.N.

    1998-01-01

    A C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language can be used to create a source code for analytical or numerical evaluations and to keep the control of the process in general

  19. Calculation of the pulsed Feynman- and Rossi-alpha formulae with delayed neutrons

    International Nuclear Information System (INIS)

    Kitamura, Y.; Pazsit, I.; Wright, J.; Yamamoto, A.; Yamane, Y.

    2005-01-01

    In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e., synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods

  20. Quantum mechanics in the cold war; Quantenmechanik im Kalten Krieg. David Bohm und Richard Feynman

    Energy Technology Data Exchange (ETDEWEB)

    Forstner, C.

    2007-07-01

    In the middle of the 20th century David Bohm and Richard Feynman developed two fundamentally different approaches of modern quantum mechanics: Bohm a realistic interpretation by means of hidden parameters and Feynman the path-integral formalism. This is by this more remarakable, because both physicists started from similar conditions and originated from similar connections. By its comparing approach this study presents more than a contribution to the history of the quantum theory. By the question for the social and cultural conditions of the formation of theories it is furthermore of science-sociological and science-theoretical interest. The in the beginning similar and later different binding of both scientists into the scientific community allows furthermore to study, which adapting pressure each group puts on the individual scientist and the fundamental parts of his research, and which new degrees of freedom in the formation of theories arise, when this constraint is cancelled.

  1. Reverse Engineering Camouflaged Sequential Integrated Circuits Without Scan Access

    OpenAIRE

    Massad, Mohamed El; Garg, Siddharth; Tripunitara, Mahesh

    2017-01-01

    Integrated circuit (IC) camouflaging is a promising technique to protect the design of a chip from reverse engineering. However, recent work has shown that even camouflaged ICs can be reverse engineered from the observed input/output behaviour of a chip using SAT solvers. However, these so-called SAT attacks have so far targeted only camouflaged combinational circuits. For camouflaged sequential circuits, the SAT attack requires that the internal state of the circuit is controllable and obser...

  2. Analytic properties of Feynman diagrams in quantum field theory

    CERN Document Server

    Todorov, I T

    1971-01-01

    Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with a

  3. A new method for the regularization of a class of divergent Feynman integrals in covariant and axial gauges

    International Nuclear Information System (INIS)

    Lee, H.C.; Milgram, M.S.

    1984-07-01

    A hybrid of dimensional and analytic regularization is used to regulate and uncover a Meijer's G-function representation for a class of massless, divergent Feynman integrals in an axial gauge. Integrals in the covariant gauge belong to a subclass and those in the light-cone gauge are reached by analytic continuation. The method decouples the physical ultraviolet and infrared singularities from the spurious axial gauge singularity but regulates all three simultaneously. For the axial gauge singularity, the new analytic method is more powerful and elegant than the old principal value prescription, but the two methods yield identical infinite as well as regular parts. It is shown that dimensional and analytic regularization can be made equivalent, implying that the former method is free from spurious γ5-anomalies and the latter preserves gauge invariance. The hybrid method permits the evaluation of integrals containing arbritrary integer powers of logarithms in the integrand by differentiation with respect to exponents. Such 'exponent derivatives' generate the same set of 'polylogs' as that generated in multi-loop integrals in perturbation theories and may be useful for solving equations in nonperturbation theories. The close relation between the method of exponent derivatives and the prescription of 't Hooft and Veltman for treating overlapping divergencies is pointed out. It is demonstrated that both methods generate functions that are free from unrecognizable logarithmic infinite parts. Nonperturbation theories expressed in terms of exponent derivatives are thus renormalizable. Some intriguing connections between nonperturbation theories and nonintegral exponents are pointed out

  4. Studies of particles statistics in one and two dimensions, based on the quantization methods of Heisenberg, Schroedinger and Feynman

    International Nuclear Information System (INIS)

    Myrheim, J.

    1993-06-01

    The thesis deals with the application of different methods to the quantization problem for system of identical particles in one and two dimensions. The standard method is the analytic quantization method due to Schroedinger, which leads to the concept of fractional statistics in one and two dimensions. Two-dimensional particles with fractional statistics are well known by the name of anyons. Two alternative quantization methods are shown by the author, the algebraic method of Heisenberg and the Feynman path integral method. The Feynman method is closely related to the Schroedinger method, whereas the Heisenberg and Schroedinger methods may give different results. The relation between the Heisenberg and Schroedinger methods is discussed. The Heisenberg method is applied to the equations of motion of vortices in superfluid helium, which have the form of Hamiltonian equations for a one-dimensional system. The same method is also discussed more generally for systems of identical particles in one and two dimensions. An application of the Feynman method to the problem of computing the equation of state for a gas of anyons is presented. 104 refs., 4 figs

  5. Single-meson inclusive cross sections and sequential decay of Reggeons, 2

    Energy Technology Data Exchange (ETDEWEB)

    Yoshida, Toshihiro

    1984-09-01

    The single-particle inclusive cross sections of pions and kaons produced from the incident particles in pp and anti pp scattering is investigated under the assumption of the sequential decay mechanism of Reggeons. The many-particle production effect and the initial-decay effect are estimated from experimental data on pion production cross section with small momentum transfer at 100 and 175 GeV/c. Their Feynman-x dependence is in good agreement with the power-law behaviours C(1-X sub(F))/sup 5/ and C(1-X sub(F))/sup 3/. Predictions are given on kaon production cross section.

  6. Solutions of the Wheeler-Feynman equations with discontinuous velocities.

    Science.gov (United States)

    de Souza, Daniel Câmara; De Luca, Jayme

    2015-01-01

    We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space.

  7. Feynman-Kac equations for reaction and diffusion processes

    Science.gov (United States)

    Hou, Ru; Deng, Weihua

    2018-04-01

    This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

  8. Statistical error estimation of the Feynman-α method using the bootstrap method

    International Nuclear Information System (INIS)

    Endo, Tomohiro; Yamamoto, Akio; Yagi, Takahiro; Pyeon, Cheol Ho

    2016-01-01

    Applicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called 'bootstrap method' standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method. (author)

  9. A Feynman-Hellmann approach to the spin structure of hadrons

    Energy Technology Data Exchange (ETDEWEB)

    Chambers, A.J. [Adelaide Univ., SA (Australia). CSSM, Dept. of Physics; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe (Japan); Collaboration: CSSM and QCDSF/UKQCD Collaborations; and others

    2014-05-15

    We perform a N{sub f}=2+1 lattice QCD simulation to determine the quark spin fractions of hadrons using the Feynman-Hellmann theorem. By introducing an external spin operator to the fermion action, the matrix elements relevant for quark spin fractions are extracted from the linear response of the hadron energies. Simulations indicate that the Feynman-Hellmann method offers statistical precision that is comparable to the standard three-point function approach, with the added benefit that it is less susceptible to excited state contamination. This suggests that the Feynman-Hellmann technique offers a promising alternative for calculations of quark line disconnected contributions to hadronic matrix elements. At the SU(3)-flavour symmetry point, we find that the connected quark spin fractions are universally in the range 55-70% for vector mesons and octet and decuplet baryons. There is an indication that the amount of spin suppression is quite sensitive to the strength of SU(3) breaking.

  10. How to solve path integrals in quantum mechanics

    International Nuclear Information System (INIS)

    Grosche, C.

    1994-10-01

    A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulae for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based. (orig.)

  11. Quadratic forms for Feynman-Kac semigroups

    International Nuclear Information System (INIS)

    Hibey, Joseph L.; Charalambous, Charalambos D.

    2006-01-01

    Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

  12. Sequential Modulations in a Combined Horizontal and Vertical Simon Task: Is There ERP Evidence for Feature Integration Effects?

    Science.gov (United States)

    Hoppe, Katharina; Küper, Kristina; Wascher, Edmund

    2017-01-01

    In the Simon task, participants respond faster when the task-irrelevant stimulus position and the response position are corresponding, for example on the same side, compared to when they have a non-corresponding relation. Interestingly, this Simon effect is reduced after non-corresponding trials. Such sequential effects can be explained in terms of a more focused processing of the relevant stimulus dimension due to increased cognitive control, which transfers from the previous non-corresponding trial (conflict adaptation effects). Alternatively, sequential modulations of the Simon effect can also be due to the degree of trial-to-trial repetitions and alternations of task features, which is confounded with the correspondence sequence (feature integration effects). In the present study, we used a spatially two-dimensional Simon task with vertical response keys to examine the contribution of adaptive cognitive control and feature integration processes to the sequential modulation of the Simon effect. The two-dimensional Simon task creates correspondences in the vertical as well as in the horizontal dimension. A trial-by-trial alternation of the spatial dimension, for example from a vertical to a horizontal stimulus presentation, generates a subset containing no complete repetitions of task features, but only complete alternations and partial repetitions, which are equally distributed over all correspondence sequences. In line with the assumed feature integration effects, we found sequential modulations of the Simon effect only when the spatial dimension repeated. At least for the horizontal dimension, this pattern was confirmed by the parietal P3b, an event-related potential that is assumed to reflect stimulus-response link processes. Contrary to conflict adaptation effects, cognitive control, measured by the fronto-central N2 component of the EEG, was not sequentially modulated. Overall, our data provide behavioral as well as electrophysiological evidence for feature

  13. A mapping between Feynman and string motivated one-loop rules in gauge theories

    International Nuclear Information System (INIS)

    Bern, Z.

    1992-01-01

    Recently, computationally efficient rules for one-loop gauge theory amplitudes have been derived from string theory. We demonstrate the relationship of the compact string organization of the amplitude to Feynman diagrams. In particular, we explicitly show how large cancellations inherent in conventional Feynman diagram computations are avoided by the string motivated rules. (orig.)

  14. Feynman rules for the Standard Model Effective Field Theory in R ξ -gauges

    Science.gov (United States)

    Dedes, A.; Materkowska, W.; Paraskevas, M.; Rosiek, J.; Suxho, K.

    2017-06-01

    We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, commonly referred to as "Warsaw basis". We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear R ξ -gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this mass basis we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available Mathematica code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.

  15. The Errors of Feynman and Hibbs

    Indian Academy of Sciences (India)

    rors simply because he was so smart. He would write down equations that got to the gist of the difficult ... work at a level somewhat below Feynman's, these fac- tors and limits and so forth are not obvious, and their ... an interview with Hibbs in which he said he's working on a book to be titled Quantum Mechanics and Path In-.

  16. Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph

    International Nuclear Information System (INIS)

    Remiddi, Ettore; Tancredi, Lorenzo

    2014-01-01

    A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two-loop sunrise graph with arbitrary masses for recovering the second-order differential equation for the scalar amplitude in d=2 dimensions, as well as a chained set of equations for all the coefficients of the expansions in (d−2). The shift from d≈2 to d≈4 dimensions is then discussed

  17. Drawing theories apart the dispersion of Feynman diagrams in postwar physics

    CERN Document Server

    Kaiser, David

    2005-01-01

    Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process.Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calcul...

  18. Exact Maximum-Entropy Estimation with Feynman Diagrams

    Science.gov (United States)

    Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.

    2018-02-01

    A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.

  19. Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane

    OpenAIRE

    Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University

    1988-01-01

    Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.

  20. Le cours de physique de Feynman

    CERN Document Server

    Feynman, Richard; Sands, Matthew

    L’ampleur du succès qu’a rencontré le « Cours de physique de Feynman » dès sa parution s’explique par son caractère fondamentalement novateur. Richard Feynman, qui fut professeur d’université dès l’âge de vingt-quatre ans, a exprimé dans ce cours, avant d’obtenir le prix Nobel de Physique, une vision expérimentale et extrêmement personnelle de l’enseignement de la physique. Cette vision a, depuis, remporté l’adhésion des physiciens du monde entier, faisant de cet ouvrage un grand classique. Ce cours en cinq volumes (Électromagnétisme 1 et 2, Mécanique 1 et 2, Mécanique quantique) s’adresse aux étudiants de tous niveaux qui y trouveront aussi bien les notions de base débarrassées de tout appareil mathématique inutile, que les avancées les plus modernes de cette science passionnante qu’est la physique. Cette nouvelle édition corrigée bénéficie d’une mise en page plus aérée pour un meilleur confort de lecture.

  1. Geometry, heat equation and path integrals on the Poincare upper half-plane

    International Nuclear Information System (INIS)

    Kubo, Reijiro.

    1987-08-01

    Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)

  2. Feynman propagator in curved space-time

    International Nuclear Information System (INIS)

    Candelas, P.; Raine, D.J.

    1977-01-01

    The Wick rotation is generalized in a covariant manner so as to apply to curved manifolds in a way that is independent of the analytic properties of the manifold. This enables us to show that various methods for defining a Feynman propagator to be found in the literature are equivalent where they are applicable. We are also able to discuss the relation between certain regularization methods that have been employed

  3. Systematic implementation of implicit regularization for multi-loop Feynman Diagrams

    International Nuclear Information System (INIS)

    Cherchiglia, Adriano Lana; Sampaio, Marcos; Nemes, Maria Carolina

    2011-01-01

    Full text: Implicit Regularization (IR) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. The essence of the method is to write the divergences in terms of loop integrals in one internal momentum which do not need to be explicitly evaluated. Moreover it acts in the physical dimension of the theory and gauge invariance is controlled by regularization dependent surface terms which when set to zero define a constrained version of IR (CIR) and deliver gauge invariant amplitudes automatically. Therefore it is in principle applicable to all physical relevant quantum field theories, supersymmetric gauge theories included. A non trivial question is whether we can generalize this program to arbitrary loop order in consonance with locality, unitarity and Lorentz invariance, especially when overlapping divergences occur. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IR program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one internal momentum. We present several examples (from 1-loop to n-loops) using scalar φ 6 3 theory in order to help the reader understand and visualize the essence of the IR program. The choice of a scalar theory does not reduce the generality of the method presented since all other physical theories can be treated within the same strategy after space time and internal algebra are performed. Another result of this contribution is to show that if the surface terms are not set to zero they will contaminate the renormalization group coefficients. Thus, we are forced to adopt CIR which is equivalent to demand momentum routing invariance

  4. Simultaneous and Sequential Integration by Cre/loxP Site-Specific Recombination in Saccharomyces cerevisiae.

    Science.gov (United States)

    Choi, Ho-Jung; Kim, Yeon-Hee

    2018-05-28

    A Cre/ loxP -δ-integration system was developed to allow sequential and simultaneous integration of a multiple gene expression cassette in Saccharomyces cerevisiae . To allow repeated integrations, the reusable Candida glabrata MARKER ( CgMARKER ) carrying loxP sequences was used, and the integrated CgMARKER was efficiently removed by inducing Cre recombinase. The XYLP and XYLB genes encoding endoxylanase and β-xylosidase, respectively, were used as model genes for xylan metabolism in this system, and the copy number of these genes was increased to 15.8 and 16.9 copies/cell, respectively, by repeated integration. This integration system is a promising approach for the easy construction of yeast strains with enhanced metabolic pathways through multicopy gene expression.

  5. A quantum formulation of the Feynman-Kac formula

    International Nuclear Information System (INIS)

    Accardi, L.

    1981-01-01

    The author discusses a formulation, in the general setting of W*- (or C*)-algebras, of the classical Feynman-Kac formula. The equivalence, in the commutative case, of the present formulation and the usual one is based on the identification between stochastic processes and local algebras. (Auth.)

  6. A partial solution for Feynman's problem: A new derivation of the Weyl equation

    Directory of Open Access Journals (Sweden)

    Atsushi Inoue

    2000-07-01

    Full Text Available Associating classical mechanics to a system of partial differential equations, we give a procedure for Feynman-type quantization of a "Schrodinger-type equation with spin." Mathematically, we construct a "good parametrix" for the Weyl equation with an external electromagnetic field. Main ingredients are (i a new interpretation of the matrix structure using superanalysis and (ii another interpretation of the method of characteristics as a quantization procedure of Feynman type.

  7. Generalized measures and the Feynman path integral

    International Nuclear Information System (INIS)

    Maslov, V.P.; Chebotarev, A.M.

    1976-01-01

    Generalizations are obtained for the earlier results by the authors concerning the inclusion of the Feynmann path integral in the momentum representation into the general integration theory. Feynmann path integrals are considered which do not represent T-products. Generalized Feynmann measure in the configuration representation is introduced

  8. Breast conserving treatment for breast cancer: dosimetric comparison of sequential versus simultaneous integrated photon boost.

    Science.gov (United States)

    Van Parijs, Hilde; Reynders, Truus; Heuninckx, Karina; Verellen, Dirk; Storme, Guy; De Ridder, Mark

    2014-01-01

    Breast conserving surgery followed by whole breast irradiation is widely accepted as standard of care for early breast cancer. Addition of a boost dose to the initial tumor area further reduces local recurrences. We investigated the dosimetric benefits of a simultaneously integrated boost (SIB) compared to a sequential boost to hypofractionate the boost volume, while maintaining normofractionation on the breast. For 10 patients 4 treatment plans were deployed, 1 with a sequential photon boost, and 3 with different SIB techniques: on a conventional linear accelerator, helical TomoTherapy, and static TomoDirect. Dosimetric comparison was performed. PTV-coverage was good in all techniques. Conformity was better with all SIB techniques compared to sequential boost (P = 0.0001). There was less dose spilling to the ipsilateral breast outside the PTVboost (P = 0.04). The dose to the organs at risk (OAR) was not influenced by SIB compared to sequential boost. Helical TomoTherapy showed a higher mean dose to the contralateral breast, but less than 5 Gy for each patient. SIB showed less dose spilling within the breast and equal dose to OAR compared to sequential boost. Both helical TomoTherapy and the conventional technique delivered acceptable dosimetry. SIB seems a safe alternative and can be implemented in clinical routine.

  9. Quantum leap from Dirac and Feynman, across the universe, to human body and mind

    CERN Document Server

    Ivancevic, Vladimir G

    2008-01-01

    This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body - all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosm

  10. Negative dimensional integrals. Pt. 1

    International Nuclear Information System (INIS)

    Halliday, I.G.; Ricotta, R.M.

    1987-01-01

    We propose a new method of evaluating integrals based on negative dimensional integration. We compute Feynman graphs by considering analytic extensions. Propagators are raised to negative integer powers and integrated over negative integer dimensions. We are left with the problem of computing polynomial integrals and summing finite series. (orig.)

  11. JaxoDraw: A graphical user interface for drawing Feynman diagrams

    Science.gov (United States)

    Binosi, D.; Theußl, L.

    2004-08-01

    JaxoDraw is a Feynman graph plotting tool written in Java. It has a complete graphical user interface that allows all actions to be carried out via mouse click-and-drag operations in a WYSIWYG fashion. Graphs may be exported to postscript/EPS format and can be saved in XML files to be used for later sessions. One of JaxoDraw's main features is the possibility to create ? code that may be used to generate graphics output, thus combining the powers of ? with those of a modern day drawing program. With JaxoDraw it becomes possible to draw even complicated Feynman diagrams with just a few mouse clicks, without the knowledge of any programming language. Program summaryTitle of program: JaxoDraw Catalogue identifier: ADUA Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUA Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar gzip file Operating system: Any Java-enabled platform, tested on Linux, Windows ME, XP, Mac OS X Programming language used: Java License: GPL Nature of problem: Existing methods for drawing Feynman diagrams usually require some 'hard-coding' in one or the other programming or scripting language. It is not very convenient and often time consuming, to generate relatively simple diagrams. Method of solution: A program is provided that allows for the interactive drawing of Feynman diagrams with a graphical user interface. The program is easy to learn and use, produces high quality output in several formats and runs on any operating system where a Java Runtime Environment is available. Number of bytes in distributed program, including test data: 2 117 863 Number of lines in distributed program, including test data: 60 000 Restrictions: Certain operations (like internal latex compilation, Postscript preview) require the execution of external commands that might not work on untested operating systems. Typical running time: As an interactive program, the running time depends on the complexity

  12. Breast Conserving Treatment for Breast Cancer: Dosimetric Comparison of Sequential versus Simultaneous Integrated Photon Boost

    Directory of Open Access Journals (Sweden)

    Hilde Van Parijs

    2014-01-01

    Full Text Available Background. Breast conserving surgery followed by whole breast irradiation is widely accepted as standard of care for early breast cancer. Addition of a boost dose to the initial tumor area further reduces local recurrences. We investigated the dosimetric benefits of a simultaneously integrated boost (SIB compared to a sequential boost to hypofractionate the boost volume, while maintaining normofractionation on the breast. Methods. For 10 patients 4 treatment plans were deployed, 1 with a sequential photon boost, and 3 with different SIB techniques: on a conventional linear accelerator, helical TomoTherapy, and static TomoDirect. Dosimetric comparison was performed. Results. PTV-coverage was good in all techniques. Conformity was better with all SIB techniques compared to sequential boost (P = 0.0001. There was less dose spilling to the ipsilateral breast outside the PTVboost (P = 0.04. The dose to the organs at risk (OAR was not influenced by SIB compared to sequential boost. Helical TomoTherapy showed a higher mean dose to the contralateral breast, but less than 5 Gy for each patient. Conclusions. SIB showed less dose spilling within the breast and equal dose to OAR compared to sequential boost. Both helical TomoTherapy and the conventional technique delivered acceptable dosimetry. SIB seems a safe alternative and can be implemented in clinical routine.

  13. The formal path integral and quantum mechanics

    International Nuclear Information System (INIS)

    Johnson-Freyd, Theo

    2010-01-01

    Given an arbitrary Lagrangian function on R d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

  14. Two loop integrals and QCD scattering

    International Nuclear Information System (INIS)

    Anastasiou, C.

    2001-04-01

    We present the techniques for the calculation of one- and two-loop integrals contributing to the virtual corrections to 2→2 scattering of massless particles. First, tensor integrals are related to scalar integrals with extra powers of propagators and higher dimension using the Schwinger representation. Integration By Parts and Lorentz Invariance recurrence relations reduce the number of independent scalar integrals to a set of master integrals for which their expansion in ε = 2 - D/2 is calculated using a combination of Feynman parameters, the Negative Dimension Integration Method, the Differential Equations Method, and Mellin-Barnes integral representations. The two-loop matrix-elements for light-quark scattering are calculated in Conventional Dimensional Regularisation by direct evaluation of the Feynman diagrams. The ultraviolet divergences are removed by renormalising with the MS-bar scheme. Finally, the infrared singular behavior is shown to be in agreement with the one anticipated by the application of Catani's formalism for the infrared divergences of generic QCD two-loop amplitudes. (author)

  15. New results for loop integrals. AMBRE, CSectors, hexagon

    International Nuclear Information System (INIS)

    Gluza, Janusz; Kajda, Krzysztof

    2009-03-01

    We report on the three Mathematica packages hexagon, CSectors, AMBRE. They are useful for the evaluation of one- and two-loop Feynman integrals with a dependence on several kinematical scales. These integrals are typically needed for LHC and ILC applications, but also for higher order corrections at meson factories. hexagon is a new package for the tensor reduction of one-loop 5-point and 6-point functions with rank R=3 and R=4, respectively; AMBRE is a tool for derivations of Mellin-Barnes representations; CSectors is an interface for the package sectordecomposition and allows a convenient, direct evaluation of tensor Feynman integrals. (orig.)

  16. Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)

    International Nuclear Information System (INIS)

    Ceder, M.

    2002-03-01

    The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods

  17. Reactivity determination in accelerator driven nuclear reactors by statistics from neutron detectors (Feynman-Alpha Method)

    Energy Technology Data Exchange (ETDEWEB)

    Ceder, M

    2002-03-01

    The Feynman-alpha method is used in traditional nuclear reactors to determine the subcritical reactivity of a system. The method is based on the measurement of the mean number and the variance of detector counts for different measurement times. The measurement is performed while a steady-state neutron flux is maintained in the reactor by an external neutron source, as a rule a radioactive source. From a plot of the variance-to-mean ratio as a function of measurement time ('gate length'), the reactivity can be determined by fitting the measured curve to the analytical solution. A new situation arises in the planned accelerator driven systems (ADS). An ADS will be run in a subcritical mode, and the steady flux will be maintained by an accelerator based source. Such a source has statistical properties that are different from those of a steady radioactive source. As one example, in a currently running European Community project for ADS research, the MUSE project, the source will be a periodically pulsed neutron generator. The theory of Feynman-alpha method needs to be extended to such nonstationary sources. There are two ways of performing and evaluating such pulsed source experiments. One is to synchronise the detector time gate start with the beginning of an incoming pulse. The Feynman-alpha method has been elaborated for such a case recently. The other method can be called stochastic pulsing. It means that there is no synchronisation between the detector time gate start and the source pulsing, i.e. the start of each measurement is chosen at a random time. The analytical solution to the Feynman-alpha formula from this latter method is the subject of this report. We have obtained an analytical Feynman-alpha formula for the case of stochastic pulsing by two different methods. One is completely based on the use of the symbolic algebra code Mathematica, whereas the other is based on complex function techniques. Closed form solutions could be obtained by both methods

  18. Quantum cosmology based on discrete Feynman paths

    International Nuclear Information System (INIS)

    Chew, Geoffrey F.

    2002-01-01

    Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''

  19. Derivation and analysis of the Feynman-alpha formula for deterministically pulsed sources

    International Nuclear Information System (INIS)

    Wright, J.; Pazsit, I.

    2004-03-01

    The purpose or this report is to give a detailed description of the calculation of the Feynman-alpha formula with deterministically pulsed sources. In contrast to previous calculations, Laplace transform and complex function methods are used to arrive at a compact solution in form of a Fourier series-like expansion. The advantage of this method is that it is capable to treat various pulse shapes. In particular, in addition to square- and Dirac delta pulses, a more realistic Gauss-shaped pulse is also considered here. The final solution of the modified variance-to-mean, that is the Feynman Y(t) function, can be quantitatively evaluated fast and with little computational effort. The analytical solutions obtained are then analysed quantitatively. The behaviour of the number or neutrons in the system is investigated in detail, together with the transient that follows the switching on of the source. An analysis of the behaviour of the Feynman Y(t) function was made with respect to the pulse width and repetition frequency. Lastly, the possibility of using me formulae for the extraction of the parameter alpha from a simulated measurement is also investigated

  20. Destructive interferences results in bosons anti bunching: refining Feynman's argument

    Science.gov (United States)

    Marchewka, Avi; Granot, Er'el

    2014-09-01

    The effect of boson bunching is frequently mentioned and discussed in the literature. This effect is the manifestation of bosons tendency to "travel" in clusters. One of the core arguments for boson bunching was formulated by Feynman in his well-known lecture series and has been frequently used ever since. By comparing the scattering probabilities of two bosons and of two distinguishable particles, he concluded: "We have the result that it is twice as likely to find two identical Bose particles scattered into the same state as you would calculate assuming the particles were different" [R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics: Quantum mechanics (Addison-Wesley, 1965)]. This argument was rooted in the scientific community (see for example [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977); W. Pauli, Exclusion Principle and Quantum Mechanics, Nobel Lecture (1946)]), however, while this sentence is completely valid, as is proved in [C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics (John Wiley & Sons, Paris, 1977)], it is not a synonym of bunching. In fact, as it is shown in this paper, wherever one of the wavefunctions has a zero, bosons can anti-bunch and fermions can bunch. It should be stressed that zeros in the wavefunctions are ubiquitous in Quantum Mechanics and therefore the effect should be common. Several scenarios are suggested to witness the effect.

  1. Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

    International Nuclear Information System (INIS)

    Tanimura, Shogo

    1992-01-01

    R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

  2. Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

    Science.gov (United States)

    Fan, Hong-yi; Xu, Xue-xiang

    2009-06-01

    By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

  3. Mean field simulation for Monte Carlo integration

    CERN Document Server

    Del Moral, Pierre

    2013-01-01

    In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Marko

  4. Some remarks on non-planar Feynman diagrams

    International Nuclear Information System (INIS)

    Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz

    2013-12-01

    Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

  5. Some remarks on non-planar Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2013-12-15

    Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

  6. Richard Feynman a life in science

    CERN Document Server

    Gribbin, John

    1998-01-01

    This text is a portrayal of one of the greatest scientists of the late 20th-century, which also provides a picture of the significant physics of the period. It combines personal anecdotes, writings and recollections with narrative. Richard Feynman's career included: war-time work on the atomic bomb at Los Alamos; a theory of quantum mechanics for which he won the Nobel prize; and major contributions to the sciences of gravity, nuclear physics and particle theory. In 1986, he was able to show that the Challenger disaster was due to the effect of cold on the booster rocket rubber sealings.

  7. Academic Training Lecture | Beyond Feynman Diagrams (1/3) | 24 April

    CERN Multimedia

    2013-01-01

    by Prof. Lance Dixon (SLAC National Accelerator Laboratory (US)). Wednesday 24 April 2013, from 11 a.m. to 12 p.m. at CERN (222-R-001 - Filtration Plant) Description: The search for new physics at the LHC, and accurate measurements of Standard Model processes, all benefit from precise theoretical predictions of collider event rates, which in turn rely on higher order computations in QCD, the theory of the strong interactions. Key ingredients for such computations are scattering amplitudes, the quantum-mechanical transition amplitudes between the incoming quarks and gluons and the outgoing produced particles. To go beyond leading order, we need both classical tree amplitudes and quantum loop amplitudes. For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events ...

  8. You err, Einstein.. Newton, Einstein, Heisenberg, and Feynman discuss quantum physics

    International Nuclear Information System (INIS)

    Fritzsch, Harald

    2008-01-01

    Harald Fritzsch and his star physicists Einstein, Heisenberg, and Feynman explain the central concept of nowadays physics, quantum mechanics, without it nothing goes in modern world. And the great Isaac newton puts the questions, which all would put

  9. Rules for integrals over products of distributions from coordinate independence of path integrals

    International Nuclear Information System (INIS)

    Kleinert, H.; Chervyakov, A.

    2001-01-01

    In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence of the path integrals. (orig.)

  10. Measurement of Feynman-x spectra of photons and neutrons in the very forward direction in deep-inelastic scattering at HERA

    Energy Technology Data Exchange (ETDEWEB)

    Andreev, V.; Belousov, A.; Fomenko, A.; Gogitidze, N.; Lebedev, A.; Malinovski, E.; Rusakov, S.; Vazdik, Y. [Lebedev Physical Institute, Moscow (Russian Federation); Baghdasaryan, A.; Zohrabyan, H. [Yerevan Physics Institute, Yerevan (Armenia); Begzsuren, K.; Ravdandorj, T.; Tseepeldorj, B. [Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar (Mongolia); Belov, P.; Brinkmann, M.; Britzger, D.; Campbell, A.J.; Dodonov, V.; Eckerlin, G.; Elsen, E.; Fleischer, M.; Gayler, J.; Ghazaryan, S.; Glazov, A.; Gouzevitch, M.; Haidt, D.; Kleinwort, C.; Krueger, K.; Levonian, S.; Lipka, K.; List, B.; List, J.; Lobodzinski, B.; Meyer, A.B.; Meyer, J.; Niebuhr, C.; Olsson, J.E.; Ozerov, D.; Pahl, P.; Petrukhin, A.; Pirumov, H.; Pitzl, D.; Placakyte, R.; Radescu, V.; Schmitt, S.; Sefkow, F.; Shushkevich, S.; South, D.; Steder, M.; Wuensch, E. [DESY, Hamburg (Germany); Boudry, V.; Specka, A. [LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau (France); Brandt, G. [Oxford University, Department of Physics, Oxford (United Kingdom); Brisson, V.; Jacquet, M.; Pascaud, C.; Zhang, Z.; Zomer, F. [LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay (France); Buniatyan, A.; Huber, F.; Sauter, M.; Schoening, A. [Universitaet Heidelberg, Physikalisches Institut, Heidelberg (Germany); Bylinkin, A.; Bystritskaya, L.; Fedotov, A.; Rostovtsev, A. [Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Cantun Avila, K.B.; Contreras, J.G. [CINVESTAV, Departamento de Fisica Aplicada, Merida, Yucatan (Mexico); Ceccopieri, F.; Favart, L.; Grebenyuk, A.; Hreus, T.; Janssen, X.; Roosen, R.; Mechelen, P. van [Brussels and Universiteit Antwerpen, Inter-University Institute for High Energies ULB-VUB, Antwerp (Belgium); Cerny, K.; Pokorny, B.; Polifka, R.; Salek, D.; Valkarova, A.; Zacek, J.; Zlebcik, R. [Charles University, Faculty of Mathematics and Physics, Prague (Czech Republic); Chekelian, V.; Grindhammer, G.; Kiesling, C. [Max-Planck-Institut fuer Physik, Munich (Germany); Dainton, J.B.; Gabathuler, E.; Greenshaw, T.; Klein, M.; Kostka, P.; Kretzschmar, J.; Laycock, P.; Maxfield, S.J.; Mehta, A.; Patel, G.D. [University of Liverpool, Department of Physics, Liverpool (United Kingdom); Daum, K.; Meyer, H. [Fachbereich C, Universitaet Wuppertal, Wuppertal (Germany); Diaconu, C.; Hoffmann, D.; Sauvan, E.; Vallee, C. [CPPM, Aix-Marseille Univ, CNRS/IN2P3, Marseille (France); Dobre, M.; Rotaru, M. [National Institute for Physics and Nuclear Engineering (NIPNE), Bucharest (Romania); Dossanov, A. [Universitaet Hamburg, Institut fuer Experimentalphysik, Hamburg (Germany); Max-Planck-Institut fuer Physik, Munich (Germany); Egli, S.; Horisberger, R. [Paul Scherrer Institut, Villigen (Switzerland); Feltesse, J.; Perez, E.; Schoeffel, L. [CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette (France); Ferencei, J. [Slovak Academy of Sciences, Institute of Experimental Physics, Kosice (Slovakia); Goerlich, L.; Mikocki, S.; Nowak, G.; Sopicki, P.; Turnau, J. [Institute for Nuclear Physics, Cracow (Poland); Grab, C. [Institut fuer Teilchenphysik, ETH, Zurich (Switzerland); Henderson, R.C.W. [University of Lancaster, Department of Physics, Lancaster (United Kingdom); Herbst, M.; Schultz-Coulon, H.C. [Kirchhoff-Institut fuer Physik, Universitaet Heidelberg, Heidelberg (Germany); Hladky, J.; Reimer, P. [Academy of Sciences of the Czech Republic, Institute of Physics, Prague (Czech Republic); Jung, H. [Brussels and Universiteit Antwerpen, Inter-University Institute for High Energies ULB-VUB, Antwerp (Belgium); DESY, Hamburg (Germany); Kapichine, M.; Lytkin, L.; Morozov, A.; Spaskov, V. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Kogler, R.; Nowak, K. [Universitaet Hamburg, Institut fuer Experimentalphysik, Hamburg (Germany); Landon, M.P.J.; Rizvi, E.; Traynor, D. [University of London, School of Physics and Astronomy, Queen Mary, London (GB); Lange, W.; Naumann, T. [DESY, Zeuthen (DE); Martyn, H.U. [I. Physikalisches Institut der RWTH, Aachen (DE); Mueller, K.; Robmann, P.; Straumann, U.; Truoel, P. [Physik-Institut der Universitaet Zuerich, Zurich (CH); Newman, P.R.; Thompson, P.D. [School of Physics and Astronomy, University of Birmingham, Birmingham (GB); Picuric, I.; Raicevic, N. [University of Montenegro, Faculty of Science, Podgorica (ME); Povh, B. [Max-Planck-Institut fuer Kernphysik, Heidelberg (DE); Sankey, D.P.C. [STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire (GB); Soloviev, Y. [DESY, Hamburg (DE); Lebedev Physical Institute, Moscow (RU); Stella, B. [Dipartimento di Fisica Universita di Roma Tre (IT); INFN Roma 3, Rome (IT); Sykora, T. [Brussels and Universiteit Antwerpen, Inter-University Institute for High Energies ULB-VUB, Antwerp (BE); Charles University, Faculty of Mathematics and Physics, Prague (CZ); Tsakov, I. [Institute for Nuclear Research and Nuclear Energy, Sofia (BG); Wegener, D. [Institut fuer Physik, TU Dortmund, Dortmund (DE); Collaboration: H1 Collaboration

    2014-06-15

    Measurements of normalised cross sections for the production of photons and neutrons at very small angles with respect to the proton beam direction in deep-inelastic ep scattering at HERA are presented as a function of the Feynman variable x{sub F} and of the centre-of-mass energy of the virtual photon-proton system W. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 131 pb{sup -1}. The measurement is restricted to photons and neutrons in the pseudorapidity range η > 7.9 and covers the range of negative four momentum transfer squared at the positron vertex 6 < Q{sup 2} < 100 GeV{sup 2}, of inelasticity 0.05 < y < 0.6 and of 70 < W < 245 GeV. To test the Feynman scaling hypothesis the W dependence of the x{sub F} dependent cross sections is investigated. Predictions of deep-inelastic scattering models and of models for hadronic interactions of high energy cosmic rays are compared to the measured cross sections. (orig.)

  11. Automatic calculation of Feynman amplitude - GRACE/CHANEL

    International Nuclear Information System (INIS)

    Kurihara, Yoshimasa

    1992-01-01

    To investigate feasibility of physics at TeV energy region, cross sections from Feynman amplitudes have to be calculated for processes with multi-particle final state. Event generation and detector simulation must also be carried out to determine a detector design and a requirement of necessary luminosity. The JLC (Japan Linear Collider) working group has developed useful software and hardware tools for above purposes. An overview of the tools developed for the physics study at the JLC is given in this report. (author) 7 refs.; 2 figs

  12. Feynman rules of quantum chromodynamics inside a hadron

    International Nuclear Information System (INIS)

    Lee, T.D.

    1979-01-01

    We start from quantum chromodynamics in a finite volume of linear size L and examine its color-dielectric constant kappa/sub L/, especially the limit kappa/sub infinity/ as L → infinity. By choosing as our standard kappa/sub L/ = 1 when L = some hadron size R, we conclude that kappa/sub infinity/ must be -2 α where α is the fine-structure constant of QCD inside the hadron. A permanent quark confinement corresponds to the limit kappa/sub infinity/ = 0. The hadrons are viewed as small domain structures (with color-dielectric constant = 1) immersed in a perfect, or nearly perfect, color-dia-electric medium, which is the vacuum. The Feynman rules of QCD inside the hadron are derived; they are found to depend on the color-dielectric constant kappa/sub infinity/ of the vacuum that lies outside. We show that, when kappa/sub infinity/ → 0, the mass of any color-nonsinglet state becomes infinity, but for color-singlet states their masses and scattering amplitudes remain finite. These new Feynman rules also depend on the hadron size R. Only at high energy and large four-momentum transfer can such R dependence be neglected and, for color-singlet states, these new rules be reduced to the usual ones

  13. A guide to Feynman diagrams in the many-body problem

    CERN Document Server

    Mattuck, Richard D

    1976-01-01

    Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. ""A great delight to read."" - Physics Today. 1974 edition.

  14. Path Integration on the Upper Half-Plane

    OpenAIRE

    Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University

    1987-01-01

    Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation ∂f/∂t=Δ_Hf can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly.

  15. Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

    Science.gov (United States)

    Danwanichakul, Panu; Glandt, Eduardo D

    2004-11-15

    We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

  16. Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

    International Nuclear Information System (INIS)

    Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

    2007-01-01

    The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

  17. Path integration on the upper half-plane

    International Nuclear Information System (INIS)

    Kubo, Reijiro.

    1987-06-01

    Feynman's path integral is considered on the Poincare upper half-plane. It is shown that the fundamental solution to the heat equation δf/δt = Δ H f can be expressed in terms of a path integral. A simple relation between the path integral and the Selberg trace formula is discussed briefly. (author)

  18. Teaching Electron--Positron--Photon Interactions with Hands-on Feynman Diagrams

    Science.gov (United States)

    Kontokostas, George; Kalkanis, George

    2013-01-01

    Feynman diagrams are introduced in many physics textbooks, such as those by Alonso and Finn and Serway, and their use in physics education has been discussed by various authors. They have an appealing simplicity and can give insight into events in the microworld. Yet students often do not understand their significance and often cannot combine the…

  19. Theory of Feynman-alpha technique with masking window for accelerator-driven systems

    International Nuclear Information System (INIS)

    Kitamura, Yasunori; Misawa, Tsuyoshi

    2017-01-01

    Highlights: • A theory of the modified Feynman-alpha technique for the ADS was developed. • The experimental conditions under which this technique works were discussed. • It is expected this technique is applied to the subcriticality monitor for the ADS. - Abstract: Recently, a modified Feynman-alpha technique for the subcritical system driven by periodically triggered neutron bursts was developed. One of the main features of this technique is utilization of a simple formula that is advantageous in evaluating the subcriticality. However, owing to the absence of the theory of this technique, this feature has not been fully investigated yet. In the present study, a theory of this technique is provided. Furthermore, the experimental conditions under which the simple formula works are discussed to apply this technique to the subcriticality monitor for the accelerator-driven system.

  20. MBsums. A Mathematica package for the representation of Mellin-Barnes integrals by multiple sums

    International Nuclear Information System (INIS)

    Ochman, Michal; Riemann, Tord

    2015-11-01

    Feynman integrals may be represented by the Mathematica package AMBRE and MB as multiple Mellin-Barnes integrals. With the Mathematica package MBsums we transform these Mellin-Barnes integrals into multiple sums.

  1. Prescriptionless light-cone integrals

    International Nuclear Information System (INIS)

    Suzuki, A.T.; Schmidt, A.G.M.

    2000-01-01

    Perturbative quantum gauge field theory as seen within the perspective of physical gauge choices such as the light-cone gauge entails the emergence of troublesome poles of the type (k.n) -α in the Feynman integrals. These come from the boson field propagator, where α=1,2,.. and n μ is the external arbitrary four-vector that defines the gauge properly. This becomes an additional hurdle in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development at this fronteer which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes to us attached to this new technique, in that not only it renders the light-cone prescriptionless but, by the very nature of it, it can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type (k.n) -α [(k-p).n] -β (β=1,2,..). In this work we demonstrate how all this can be done. (orig.)

  2. ALOHA: Automatic libraries of helicity amplitudes for Feynman diagram computations

    Science.gov (United States)

    de Aquino, Priscila; Link, William; Maltoni, Fabio; Mattelaer, Olivier; Stelzer, Tim

    2012-10-01

    We present an application that automatically writes the HELAS (HELicity Amplitude Subroutines) library corresponding to the Feynman rules of any quantum field theory Lagrangian. The code is written in Python and takes the Universal FeynRules Output (UFO) as an input. From this input it produces the complete set of routines, wave-functions and amplitudes, that are needed for the computation of Feynman diagrams at leading as well as at higher orders. The representation is language independent and currently it can output routines in Fortran, C++, and Python. A few sample applications implemented in the MADGRAPH 5 framework are presented. Program summary Program title: ALOHA Catalogue identifier: AEMS_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: http://www.opensource.org/licenses/UoI-NCSA.php No. of lines in distributed program, including test data, etc.: 6094320 No. of bytes in distributed program, including test data, etc.: 7479819 Distribution format: tar.gz Programming language: Python2.6 Computer: 32/64 bit Operating system: Linux/Mac/Windows RAM: 512 Mbytes Classification: 4.4, 11.6 Nature of problem: An effcient numerical evaluation of a squared matrix element can be done with the help of the helicity routines implemented in the HELAS library [1]. This static library contains a limited number of helicity functions and is therefore not always able to provide the needed routine in the presence of an arbitrary interaction. This program provides a way to automatically create the corresponding routines for any given model. Solution method: ALOHA takes the Feynman rules associated to the vertex obtained from the model information (in the UFO format [2]), and multiplies it by the different wavefunctions or propagators. As a result the analytical expression of the helicity routines is obtained. Subsequently, this expression is

  3. On the classical Maxwell-Lorentz electrodynamics, the electron inertia problem, and the Feynman proper time paradigm

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Bogolubov, J.R.

    2016-01-01

    The classical Maxwell electromagnetic field and the Lorentz-type force equations are rederived in the framework of the Feynman proper time paradigm and the related vacuum field theory approach. The classical Ampere law origin is rederived, and its relationship with the Feynman proper time paradigm is discussed. The electron inertia problem is analyzed in detail within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle of stochastic electrodynamics. The modified Abraham-Lorentz damping radiation force is derived and the electromagnetic electron mass origin is argued

  4. The Hellmann–Feynman theorem, the comparison theorem, and the envelope theory

    Directory of Open Access Journals (Sweden)

    Claude Semay

    2015-01-01

    Full Text Available The envelope theory is a convenient method to compute approximate solutions for bound state equations in quantum mechanics. It is shown that these approximate solutions obey a kind of Hellmann–Feynman theorem, and that the comparison theorem can be applied to these approximate solutions for two ordered Hamiltonians.

  5. Asymptotic expansions of Feynman diagrams and the Mellin-Barnes representation

    International Nuclear Information System (INIS)

    Friot, Samuel; Greynat, David

    2007-01-01

    In this talk, we describe part of our recent work [S. Friot, D. Greynat and E. de Rafael, Phys. Lett. B 628 (2005) 73 [ (arXiv:hep-ph/0505038)] (see also [S. Friot, PhD Thesis (2005); D. Greynat, PhD Thesis (2005)]) that gives new results in the context of asymptotic expansions of Feynman diagrams using the Mellin-Barnes representation

  6. Relation between Feynman Cycles and Off-Diagonal Long-Range Order

    International Nuclear Information System (INIS)

    Ueltschi, Daniel

    2006-01-01

    The usual order parameter for Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We discuss its validity with the help of rigorous results and heuristic arguments. The conclusion is that infinite cycles do not always represent the Bose condensate

  7. Branching trajectory continual integral

    International Nuclear Information System (INIS)

    Maslov, V.P.; Chebotarev, A.M.

    1980-01-01

    Heuristic definition of the Feynman continual integral over branching trajectories is suggested which makes it possible to obtain in the closed form the solution of the Cauchy problem for the model Hartree equation. A number of properties of the solution is derived from an integral representation. In particular, the quasiclassical asymptotics, exact solution in the gaussian case and perturbation theory series are described. The existence theorem for the simpliest continual integral over branching trajectories is proved [ru

  8. Closure of the gauge algebra, generalized Lie equations and Feynman rules

    International Nuclear Information System (INIS)

    Batalin, I.A.

    1984-01-01

    A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one. (orig.)

  9. Axiomatic derivation of Feynman rules and related topics

    International Nuclear Information System (INIS)

    Dorfmeister, G.K.

    1992-01-01

    Previous results in axiomatic field theory by Steinmann and Epstein-Glaser establish the existence of the retarded and time ordered Green's functions in every order of perturbation. To connect these Green's functions with the ones calculated in canonical field theories via the Feynman rules, one has to consistently build them not just for every order of perturbation but for each specific graph. (open-quotes Consisentlyclose quotes means here that the Green functions associated with two open-quotes smallclose quotes graphs build up to the Green's functions of the open-quotes bigclose quotes graph formed by connecting the two open-quotes smallclose quotes ones). This paper shows that this can indeed be done; that in this sense the Feynman rules of perturbative Lagrangian field theory can be derived from the abstract, but physically very basic, principles of axiomatic field theory. All results hold only for massive field theories. The LSZ formalism, to the best knowledge of the author, has so far not been modified to admit mass zero fields. To make the representation simpler and more transparent, the author restricts the discussion to a single component, scalar Φ 4 interaction which is a part of the Standard Model of Particle Physics. Motivated by its role in particle physics, the author complements the perturbative study of Φ 4 -theory by reviewing the status of non-perturbative solutions to the theory in the final chapter

  10. Hellmann–Feynman connection for the relative Fisher information

    Energy Technology Data Exchange (ETDEWEB)

    Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com [Systems Research Corporation, Aundh, Pune 411007 (India); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [IFLP, National University La Plata & National Research (CONICET) C. C., 727 1900, La Plata (Argentina)

    2015-08-15

    The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS link and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.

  11. Loopedia, a database for loop integrals

    Science.gov (United States)

    Bogner, C.; Borowka, S.; Hahn, T.; Heinrich, G.; Jones, S. P.; Kerner, M.; von Manteuffel, A.; Michel, M.; Panzer, E.; Papara, V.

    2018-04-01

    Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of INSPIRE or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology.

  12. Extended Hellmann-Feynman theorem for degenerate eigenstates

    Science.gov (United States)

    Zhang, G. P.; George, Thomas F.

    2004-04-01

    In a previous paper, we reported a failure of the traditional Hellmann-Feynman theorem (HFT) for degenerate eigenstates. This has generated enormous interest among different groups. In four independent papers by Fernandez, by Balawender, Hola, and March, by Vatsya, and by Alon and Cederbaum, an elegant method to solve the problem was devised. The main idea is that one has to construct and diagonalize the force matrix for the degenerate case, and only the eigenforces are well defined. We believe this is an important extension to HFT. Using our previous example for an energy level of fivefold degeneracy, we find that those eigenforces correctly reflect the symmetry of the molecule.

  13. A newly designed multichannel scaling system: Validated by Feynman-α experiment in EHWZPR

    Energy Technology Data Exchange (ETDEWEB)

    Arkani, Mohammad, E-mail: markani@aeoi.org.ir; Mataji-Kojouri, Naimeddin

    2016-08-15

    Highlights: • An embedded measuring system with enhanced operational capabilities is introduced to the scientists. • The design is low cost and reprogrammable. • The system design is dedicated to multi-detector experiments with huge data collection. • Non count loss effect Feynman-α experiment is performed in EHWZPR. • The results is compared with endogenous/inherent pulsed neutron source experiment. - Abstract: In this work, an embedded multi-input multi-million-channel MCS in a newly design is constructed for multi-detector experimental research applications. Important characteristics of the system are possible to be tuned based on experimental case studies utilizing the reprogrammable nature of the silicon. By means of differentiation of the integrated counts registered in memory, this system is featured as a zero channel advance time measuring tool ideal for experiments on time correlated random processes. Using this equipment, Feynman-α experiment is performed in Esfahan Heavy Water Zero Power Reactor (EHWZPR) utilizing three different in-core neutron detectors. One million channel data is collected by the system in 5 ms gate time from each neutron detector simultaneously. As heavy water moderated reactors are significantly slow systems, a huge number of data channels is required to be collected. Then, by making in use of bunching method, the data is analyzed and prompt neutron decay constant of the system is estimated for each neutron detector positioned in the core. The results are compared with the information provided by endogenous pulsed neutron source experiment and a good agreement is seen within the statistical uncertainties of the results. This equipment makes further research in depth possible in a range of stochastic experiments in nuclear physics such as cross correlation analysis of multi-detector experiments.

  14. The dependence of J/ψ-nucleon inelastic cross section on the Feynman variable

    International Nuclear Information System (INIS)

    Duan Chungui; Liu Na; Miao Wendan

    2011-01-01

    By means of two typical sets of nuclear parton distribution functions, meanwhile taking account of the energy loss of the beam proton and the nuclear absorption of the charmonium states traversing the nuclear matter in the uniform framework of the Glauber model, a leading order phenomenological analysis is given in the color evaporation model of the E866 experimental data on J/ψ production differential cross section ratios R Fe/Be (x F ). It is shown that the energy loss effect of beam proton on R Fe/Be (x F ) is more important than the nuclear effects on parton distribution functions in the high Feynman variable x F region. It is found that the J/ψ-nucleon inelastic cross section depends on the Feynman variable x F and increases linearly with x F in the region x F > 0.2. (authors)

  15. Advanced quantum theory and its applications through Feynman diagrams

    International Nuclear Information System (INIS)

    Scadron, M.D.

    1979-01-01

    The two themes of scattering diagrams and the fundamental forces characterize this book. Transformation theory is developed to review the concepts of nonrelativistic quantum mechanics and to formulate the relativistic Klein-Gordon, Maxwell, and Dirac wave equations for relativistic spin-0, massless spin-1, and spin-1/2 particles, respectively. The language of group theory is used to write relativistic Lorentz transformations in a form similar to ordinary rotations and to describe the important discrete symmetries of C, P, and T. Then quantum mechanics is reformulated in the language of scattering theory, with the momentum-space S matrix replacing the coordinate-space hamiltonian as the central dynamical operator. Nonrelativistic perturbation scattering diagrams are then developed, and simple applications given for nuclear, atomic, and solid-state scattering problems. Next, relativistic scattering diagrams built up from covariant Feynman propagators and vertices in a manner consistent with the CPT theorem are considered. The theory is systematically applied to the lowest-order fundamental electromagnetic, strong, weak, and gravitational interactions. Finally, the use of higher-order Feynman diagrams to explain more detailed aspects of quantum electrodynamics (QED) and strong-interaction elementary-particle physics is surveyed. Throughout, the notion of currents is used to exploit the underlying symmetries and dynamical interactions of the various quantum forces. 258 references, 77 figures, 1 table

  16. Specific features of the REDUCE system and calculation of QCD Feynman graphs

    International Nuclear Information System (INIS)

    Dulyan, L.S.

    1990-01-01

    The ways and methods used in calculation of one class of the QCD Feynman graphs with the help of the REDUCE system are described. It is shown how by introducing new constructions and operations the user could avoid difficulties connected with specific restrictions and features of the REDUCE system

  17. Eyewitness confidence in simultaneous and sequential lineups: a criterion shift account for sequential mistaken identification overconfidence.

    Science.gov (United States)

    Dobolyi, David G; Dodson, Chad S

    2013-12-01

    Confidence judgments for eyewitness identifications play an integral role in determining guilt during legal proceedings. Past research has shown that confidence in positive identifications is strongly associated with accuracy. Using a standard lineup recognition paradigm, we investigated accuracy using signal detection and ROC analyses, along with the tendency to choose a face with both simultaneous and sequential lineups. We replicated past findings of reduced rates of choosing with sequential as compared to simultaneous lineups, but notably found an accuracy advantage in favor of simultaneous lineups. Moreover, our analysis of the confidence-accuracy relationship revealed two key findings. First, we observed a sequential mistaken identification overconfidence effect: despite an overall reduction in false alarms, confidence for false alarms that did occur was higher with sequential lineups than with simultaneous lineups, with no differences in confidence for correct identifications. This sequential mistaken identification overconfidence effect is an expected byproduct of the use of a more conservative identification criterion with sequential than with simultaneous lineups. Second, we found a steady drop in confidence for mistaken identifications (i.e., foil identifications and false alarms) from the first to the last face in sequential lineups, whereas confidence in and accuracy of correct identifications remained relatively stable. Overall, we observed that sequential lineups are both less accurate and produce higher confidence false identifications than do simultaneous lineups. Given the increasing prominence of sequential lineups in our legal system, our data argue for increased scrutiny and possibly a wholesale reevaluation of this lineup format. PsycINFO Database Record (c) 2013 APA, all rights reserved.

  18. Do we need Feynman diagrams for higher order perturbation theory?

    International Nuclear Information System (INIS)

    Jora, Renata

    2012-01-01

    We compute the two loop and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

  19. One-loop tensor Feynman integral reduction with signed minors

    DEFF Research Database (Denmark)

    Fleischer, Jochem; Riemann, Tord; Yundin, Valery

    2012-01-01

    of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically......We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms...

  20. Vous voulez rire, monsieur Feynman !

    CERN Document Server

    Feynman, Richard P

    2000-01-01

    Richard Feynman fut un scientifique hors norme. Non seulement il contribua en profondeur à la grande aventure de la physique des particules élémentaires, depuis la fabrication de la bombe atomique pendant la guerre alors qu'il n'a pas 25 ans, jusqu'à ses diagrammes qui permettent d'y voir un peu plus clair dans les processus physiques de base. Non seulement il fut un professeur génial, n'hésitant pas à faire le clown pour garder l'attention de ses étudiants et à simplifier pour aller à l'essentiel. Mais il mena une vie excentrique - collectionneur, bouffon, impertinent, joueur de bongo, amateur de strip-tease, séducteur impénitent, déchiffreur de codes secrets et de textes mayas, explorateur en Asie centrale -, qu'il raconte ici avec l'humour du gamin des rues de New York qu'il n'a jamais cessé d'être.

  1. Experimental demonstration of the finite measurement time effect on the Feynman-{alpha} technique

    Energy Technology Data Exchange (ETDEWEB)

    Wallerbos, E.J.M.; Hoogenboom, J.E

    1998-09-01

    The reactivity of a subcritical system is determined by fitting two different theoretical models to a measured Feynman-{alpha} curve. The first model is the expression usually found in the literature, which can be shown to be the expectation value of the experimental quality if the measurement time is infinite. The second model is a new expression which is the expectation value of the experimental quantity for a finite measurement time. The reactivity inferred with the new model is seen to be independent of the length of the fitting interval, whereas the reactivity inferred with the conventional model is seen to vary. This difference demonstrates the effect of the finite measurement time. As a reference, the reactivity is also measured with the pulsed-neutron source method. It is seen to be in good agreement with the reactivity obtained with the Feynman-{alpha} technique when the new expression is applied.

  2. Sequential and simultaneous choices: testing the diet selection and sequential choice models.

    Science.gov (United States)

    Freidin, Esteban; Aw, Justine; Kacelnik, Alex

    2009-03-01

    We investigate simultaneous and sequential choices in starlings, using Charnov's Diet Choice Model (DCM) and Shapiro, Siller and Kacelnik's Sequential Choice Model (SCM) to integrate function and mechanism. During a training phase, starlings encountered one food-related option per trial (A, B or R) in random sequence and with equal probability. A and B delivered food rewards after programmed delays (shorter for A), while R ('rejection') moved directly to the next trial without reward. In this phase we measured latencies to respond. In a later, choice, phase, birds encountered the pairs A-B, A-R and B-R, the first implementing a simultaneous choice and the second and third sequential choices. The DCM predicts when R should be chosen to maximize intake rate, and SCM uses latencies of the training phase to predict choices between any pair of options in the choice phase. The predictions of both models coincided, and both successfully predicted the birds' preferences. The DCM does not deal with partial preferences, while the SCM does, and experimental results were strongly correlated to this model's predictions. We believe that the SCM may expose a very general mechanism of animal choice, and that its wider domain of success reflects the greater ecological significance of sequential over simultaneous choices.

  3. S-matrix, Feynman zigzag and Einstein correlation

    International Nuclear Information System (INIS)

    Costa de Beauregard, O.

    1978-01-01

    An inherent binding between Einstein correlations and the S-matrix formalism entails full relativistic covariance, complete time symmetry, and spacelike connexions via Feynman zigzags. The relay is in the past for predictive correlations between future measurements, and in the future for retrodictive correlations between past preparations (Pflegor and Mandel). An analogy and a partial binding exist between intrinsic symmetry together with factlike asymmetry of (1) 'blind statistical' prediction and retrodiction (retarded and advanced waves, information as cognizance and as will) and (2) positive and negative frequencies (particles and antiparticles). As advanced waves are required for completeness of expansions, 'antiphysics' obeying blind statistical retrodiction should show up in appropriate contexts, 'parapsychology' being submitted as one of them. (Auth.)

  4. One-loop tensor Feynman integral reduction with signed minors

    International Nuclear Information System (INIS)

    Fleischer, J.; Yundin, V.

    2011-12-01

    We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

  5. One-loop tensor Feynman integral reduction with signed minors

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, V. [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center

    2011-12-15

    We present an algebraic approach to one-loop tensor integral reduction. The integrals are presented in terms of scalar one- to four-point functions. The reduction is worked out explicitly until five-point functions of rank five. The numerical C++ package PJFry evaluates tensor coefficients in terms of a basis of scalar integrals, which is provided by an external library, e.g. QCDLoop. We shortly describe installation and use of PJFry. Examples for numerical results are shown, including a special treatment for small or vanishing inverse four-point Gram determinants. An extremely efficient application of the formalism is the immediate evaluation of complete contractions of the tensor integrals with external momenta. This leads to the problem of evaluating sums over products of signed minors with scalar products of chords. Chords are differences of external momenta. These sums may be evaluated analytically in a systematic way. The final expressions for the numerical evaluation are then compact combinations of the contributing basic scalar functions. (orig.)

  6. Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

    International Nuclear Information System (INIS)

    Bluemlein, Johannes; Phan, Khiem Hong; Vietnam National Univ., Ho Chi Minh City; Riemann, Tord; Silesia Univ., Chorzow

    2017-11-01

    Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions 2 F 1 and F 1 . Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

  7. Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d

    Energy Technology Data Exchange (ETDEWEB)

    Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Phan, Khiem Hong [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Vietnam National Univ., Ho Chi Minh City (Viet Nam). Univ. of Science; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Silesia Univ., Chorzow (Poland). Inst. of Physics

    2017-11-15

    Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension d in terms of (generalized) hypergeometric functions {sub 2}F{sub 1} and F{sub 1}. Values at asymptotic or exceptional kinematic points as well as expansions around the singular points at d=4+2n, n non-negative integers, may be derived from the representations easily. The Feynman integrals studied here may be used as building blocks for the calculation of one-loop and higher-loop scalar and tensor amplitudes. From the recursion relation presented, higher n-point functions may be obtained in a straightforward manner.

  8. Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

    International Nuclear Information System (INIS)

    Di Ventra, Massimiliano; Pantelides, Sokrates T.

    2000-01-01

    The conventional Hellmann-Feynman theorem for the definition of forces on nuclei is not directly applicable to quantum time-dependent and transport problems. We present a rigorous derivation of a general Hellmann-Feynman-like theorem that applies to all quantum mechanical systems and reduces to well-known results for ground-state problems. It provides a rigorous definition of forces in time-dependent and transport problems. Explicit forms of Pulay-like forces are derived and the conditions for them to be zero are identified. A practical scheme for ab initio calculations of current-induced forces is described and the study of the transfer of a Si atom between two electrodes is presented as an example. (c) 2000 The American Physical Society

  9. Path integral quantization in the temporal gauge

    International Nuclear Information System (INIS)

    Scholz, B.; Steiner, F.

    1983-06-01

    The quantization of non-Abelian gauge theories in the temporal gauge is studied within Feynman's path integral approach. The standard asymptotic boundary conditions are only imposed on the transverse gauge fields. The fictituous longitudinal gauge quanta are eliminated asymptotically by modified boundary conditions. This abolishes the residual time-independent gauge transformations and leads to a unique fixing of the temporal gauge. The resulting path integral for the generating functional respects automatically Gauss's law. The correct gauge field propagator is derived. It does not suffer from gauge singularities at n x k = 0 present in the usual treatment of axial gauges. The standard principal value prescription does not work. As a check, the Wilson loop in temporal gauge is calculated with the new propagator. To second order (and to all orders in the Abelian case) the result agrees with the one obtained in the Feynman and Coulomb gauge. (orig.)

  10. Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation

    International Nuclear Information System (INIS)

    Aparicio, J.P.; Garcia Alvarez, E.T.

    1995-01-01

    The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism. ((orig.))

  11. A Bayesian Theory of Sequential Causal Learning and Abstract Transfer.

    Science.gov (United States)

    Lu, Hongjing; Rojas, Randall R; Beckers, Tom; Yuille, Alan L

    2016-03-01

    Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause-effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with entirely different cues, suggesting that learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre-training (or even post-training) can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables (e.g., binary vs. continuous) to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue-outcome co-occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge. Copyright © 2015

  12. Feynman graphs and gauge theories for experimental physicists. 2. rev. ed.

    International Nuclear Information System (INIS)

    Schmueser, P.

    1995-01-01

    This book is an introduction to the foundations of quantum field theory with special regards to gauge theory. After a general introduction to relativistic wave equations the concept of Feynman graphs is introduced. Then after an introduction to the phenomenology of weak interactions and the principle of gauge invariance the standard model of the electroweak interaction is presented. Finally quantum chromodynamics is described. Every chapter contains exercise problems. (HSI)

  13. Anomaly detection in random heterogeneous media Feynman-Kac formulae, stochastic homogenization and statistical inversion

    CERN Document Server

    Simon, Martin

    2015-01-01

    This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem.   Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems  Targe...

  14. Projection operator and propagator for an arbitrary integral spin

    CERN Document Server

    Huang Shi Zhong; Wu Ning; Zheng Zhi Peng

    2002-01-01

    Based on the solution of the Bargmann-Wigner equation for an arbitrary integral spin, a direct derivation of the projection operator and propagator for an arbitrary integral spin is presented. The explicit form for the spin projection operators constructed by Behrends and Fronsdal is confirmed. The commutation rules and a general expression for the Feynman propagator for a free particle of arbitrary integral spin are deduced

  15. Computation of Groebner bases for two-loop propagator type integrals

    International Nuclear Information System (INIS)

    Tarasov, O.V.

    2004-01-01

    The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases

  16. Computation of Groebner bases for two-loop propagator type integrals

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, O.V. [DESY Zeuthen, Theory Group, Deutsches Elektronen Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen (Germany)]. E-mail: tarasov@ifh.de

    2004-11-21

    The Groebner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Groebner bases for all integrals with 1PI topologies and present explicit content of the Groebner bases.

  17. New analytical treatment for a kind of two dimensional integrals in ion-atom collisions

    International Nuclear Information System (INIS)

    Yang Qifeng; Kuang Yurang

    1994-01-01

    A kind of two-dimensional integrals, separated from two-center matrix elements in ion-atom collisions, is analytically integrated by introducing the Laplace transform into the integrals and expressed by the modified Bessel functions. The traditional Feynman transform is very complicated for this kind of more general integrals related to the excited state capture

  18. A comparison of sequential and information-based methods for determining the co-integration rank in heteroskedastic VAR MODELS

    DEFF Research Database (Denmark)

    Cavaliere, Giuseppe; Angelis, Luca De; Rahbek, Anders

    2015-01-01

    In this article, we investigate the behaviour of a number of methods for estimating the co-integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular, we compare the efficacy of the most widely used information criteria, such as Akaike Information Criterion....... The relative finite-sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC-based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms......-based method to over-estimate the co-integration rank in relatively small sample sizes....

  19. Numerical approach to one-loop integrals

    International Nuclear Information System (INIS)

    Fujimoto, Junpei; Shimizu, Yoshimitsu; Kato, Kiyoshi; Oyanagi, Yoshio.

    1992-01-01

    Two numerical methods are proposed for the calculation of one-loop scalar integrals. In the first method, the singularity is cancelled by the symmetrization of the integrand and the integration is done by a Monte-Carlo method. In the second one, after the transform of the integrand into a standard form, the integral is reduced into a regular numerical integral. These methods provide us practical tools to evaluate one-loop Feynman diagrams with desired numerical accuracy. They are extended to the integral with numerator and the treatment of the one-loop virtual correction to the cross section is also presented. (author)

  20. Feynman variance-to-mean in the context of passive neutron coincidence counting

    Energy Technology Data Exchange (ETDEWEB)

    Croft, S., E-mail: scroft@lanl.gov [Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545 (United States); Favalli, A.; Hauck, D.K.; Henzlova, D.; Santi, P.A. [Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545 (United States)

    2012-09-11

    Passive Neutron Coincidence Counting (PNCC) based on shift register autocorrelation time analysis of the detected neutron pulse train is an important Nondestructive Assay (NDA) method. It is used extensively in the quantification of plutonium and other spontaneously fissile materials for purposes of nuclear materials accountancy. In addition to the totals count rate, which is also referred to as the singles, gross or trigger rate, a quantity known as the reals coincidence rate, also called the pairs or doubles, is obtained from the difference between the measured neutron multiplicities in two measurement gates triggered by the incoming events on the pulse train. The reals rate is a measure of the number of time correlated pairs present on the pulse train and this can be related to the fission rates (and hence material mass) since fissions emit neutrons in bursts which are also detected in characteristic clusters. A closely related measurement objective is the determination of the reactivity of systems as they approach criticality. In this field an alternative autocorrelation signature is popular, the so called Feynman variance-to-mean technique which makes use of the multiplicity histogram formed the periodic, or clock-triggered opening of a coincidence gate. Workers in these two application areas share common challenges and improvement opportunities but are often separated by tradition, problem focus and technical language. The purpose of this paper is to recognize the close link between the Feynman variance-to-mean metric and traditional PNCC using shift register logic applied to correlated pulse trains. We, show using relationships for the late-gate (or accidentals) histogram recorded using a multiplicity shift register, how the Feynman Y-statistic, defined as the excess variance-to-mean ratio, can be expressed in terms of the singles and doubles rates familiar to the safeguards and waste assay communities. These two specialisms now have a direct bridge between

  1. Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Bluemlein, Johannes; Klein, Sebastian; Schneider, Carsten

    2010-01-01

    By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion.

  2. Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

    International Nuclear Information System (INIS)

    Giraud, O; Thain, A; Hannay, J H

    2004-01-01

    The shrunk loop theorem proved here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian (or Feynman) path of a given 'duration' might have on the twice punctured plane (plane with two marked points). The result is expressed as a 'scattering' series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schroedinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes and (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts from the Stovicek scattering expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two-dimensional integration, distilling the topology from the geometry

  3. BOOK REVIEW: Path Integrals in Field Theory: An Introduction

    Science.gov (United States)

    Ryder, Lewis

    2004-06-01

    In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed

  4. Magic identities for conformal four-point integrals

    International Nuclear Information System (INIS)

    Drummond, James M.; Henn, Johannes; Smirnov, Vladimir A.; Sokatchev, Emery

    2007-01-01

    We propose an iterative procedure for constructing classes of off-shell four-point conformal integrals which are identical. The proof of the identity is based on the conformal properties of a subintegral common for the whole class. The simplest example are the so-called 'triple scalar box' and 'tennis court' integrals. In this case we also give an independent proof using the method of Mellin-Barnes representation which can be applied in a similar way for general off-shell Feynman integrals

  5. Improved parametrization of K+ production in p-Be collisions at low energy using Feynman scaling

    International Nuclear Information System (INIS)

    Mariani, C.; Cheng, G.; Shaevitz, M. H.; Conrad, J. M.

    2011-01-01

    This paper describes an improved parametrization for proton-beryllium production of secondary K + mesons for experiments with primary proton beams from 8.89 to 24 GeV/c. The parametrization is based on Feynman scaling in which the invariant cross section is described as a function of x F and p T . This method is theoretically motivated and provides a better description of the energy dependence of kaon production at low beam energies than other parametrizations such as the commonly used modified Sanford-Wang model. This Feynman scaling parametrization has been used for the simulation of the neutrino flux from the Booster Neutrino Beam at Fermilab and has been shown to agree with the neutrino interaction data from the SciBooNE experiment. This parametrization will also be useful for future neutrino experiments with low primary beam energies, such as those planned for the Project X accelerator.

  6. Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

    Science.gov (United States)

    Eden, Burkhard; Smirnov, Vladimir A.

    2016-10-01

    We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

  7. Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität zu Berlin,Zum großen Windkanal 6, 12489 Berlin (Germany); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics, Moscow State University,119992 Moscow (Russian Federation)

    2016-10-21

    We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

  8. Modern summation methods and the computation of 2- and 3-loop Feynman diagrams

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Klein, Sebastian

    2010-06-01

    By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)

  9. Modern summation methods and the computation of 2- and 3-loop Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Linz Univ. (AT). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, Sebastian [RWTH Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie

    2010-06-15

    By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with all our concrete calculations of 2-loop and 3-loop massive single scale Feynman diagrams with local operator insertion. (orig.)

  10. Bioremediation of PAHs contaminated river sediment by an integrated approach with sequential injection of co-substrate and electron acceptor: Lab-scale study

    International Nuclear Information System (INIS)

    Liu, Tongzhou; Zhang, Zhen; Dong, Wenyi; Wu, Xiaojing; Wang, Hongjie

    2017-01-01

    In this study, the feasibility of employing an integrated bioremediation approach in contaminated river sediment was evaluated. Sequential addition of co-substrate (acetate) and electron acceptor (NO 3 − ) in a two-phase treatment was capable of effectively removing polycyclic aromatic hydrocarbons (PAHs) in river sediment. The residual concentration of total PAHs decreased to far below effect range low (ERL) value within 91 days of incubation, at which concentration it could rarely pose biological impairment. The biodegradation of high molecular weight PAHs were found to be mainly occurred in the sediment treated with co-substrates (i.e. acetate or methanol), in which acetate was found to be more suitable for PAHs degradation. The role of co-substrates in influencing PAHs biodegradation was tentatively discussed herein. Additionally, the sediment odorous problem and blackish appearance were intensively addressed by NO 3 − injection. The results of this study demonstrated that integrating two or more approaches/processes would be a helpful option in sediment remediation. It can lead to a more effective remediation performance, handle multiple contamination issues, as well as mitigate environmental risks caused by one of the single methods. - Highlights: • Sequential addition of acetate and NO 3 − removed PAHs and mitigated sediment odor. • Acetate is a suitable co-substrate used for PAHs degradation in river sediment. • NO 3 − Injection was effective for sediment odor and blackish appearance mitigation. • Integrated method is suggested in complicated real case with multi-remedial target. - Sequential addition of co-substrate and electron acceptor was capable of effectively removing PAHs and addressing sediment odorous problem and blackish appearance.

  11. Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

    International Nuclear Information System (INIS)

    Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

    2017-06-01

    A number of irreducible master integrals for L-loop sunrise and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via the Mellin-Barnes representation.

  12. Feynman diagrams sampling for quantum field theories on the QPACE 2 supercomputer

    Energy Technology Data Exchange (ETDEWEB)

    Rappl, Florian

    2016-08-01

    This work discusses the application of Feynman diagram sampling in quantum field theories. The method uses a computer simulation to sample the diagrammatic space obtained in a series expansion. For running large physical simulations powerful computers are obligatory, effectively splitting the thesis in two parts. The first part deals with the method of Feynman diagram sampling. Here the theoretical background of the method itself is discussed. Additionally, important statistical concepts and the theory of the strong force, quantum chromodynamics, are introduced. This sets the context of the simulations. We create and evaluate a variety of models to estimate the applicability of diagrammatic methods. The method is then applied to sample the perturbative expansion of the vertex correction. In the end we obtain the value for the anomalous magnetic moment of the electron. The second part looks at the QPACE 2 supercomputer. This includes a short introduction to supercomputers in general, as well as a closer look at the architecture and the cooling system of QPACE 2. Guiding benchmarks of the InfiniBand network are presented. At the core of this part, a collection of best practices and useful programming concepts are outlined, which enables the development of efficient, yet easily portable, applications for the QPACE 2 system.

  13. Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields

    International Nuclear Information System (INIS)

    Albeverio, S.; Brzezniak, Z.

    1994-01-01

    We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)

  14. Covariant path integrals on hyperbolic surfaces

    Science.gov (United States)

    Schaefer, Joe

    1997-11-01

    DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377-397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli-DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman-Kac formula for the automorphic Schrödinger equation on the Riemann surface ΓH. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47-90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319-328 (1987).

  15. On the calculation of soft phase space integral

    International Nuclear Information System (INIS)

    Zhu, Hua Xing

    2015-01-01

    The recent discovery of the Higgs boson at the LHC attracts much attention to the precise calculation of its production cross section in quantum chromodynamics. In this work, we discuss the calculation of soft triple-emission phase space integral, which is an essential ingredient in the recently calculated soft-virtual corrections to Higgs boson production at next-to-next-to-next-to-leading order. The main techniques used this calculation are method of differential equation for Feynman integral, and integration of harmonic polylogarithms.

  16. Feynman graph derivation of Einstein quadrupole formula

    International Nuclear Information System (INIS)

    Dass, N.D.H.; Soni, V.

    1980-11-01

    The one graviton transition operator, and consequently, the classical energy loss formula for gravitational radiation are derived from the Feynman graphs of helicity +- 2 theories of gravitation. The calculations are done both for the case of electromagnetic and gravitational scattering. The departure of the in and out states from plane waves owing to the long range nature of gravitation is taken into account to improve the Born approximation calculations. This also includes a long range modification of the graviton wave function which is shown to be equivalent to the classical problem of the true light cones deviating logarithmically at large distances from the flat space light cones. The transition from the S-matrix elements calculated graphically to the graviton transition operator is done by using complimentarity of space-time and momentum descriptions. The energy loss formula derived originally by Einstein is shown to be correct. (Auth.)

  17. Feynman quasi probability distribution for spin-(1/2), and its generalizations

    International Nuclear Information System (INIS)

    Colucci, M.

    1999-01-01

    It has been examined the Feynman's paper Negative probability, in which, after a discussion about the possibility of attributing a real physical meaning to quasi probability distributions, he introduces a new kind of distribution for spin-(1/2), with a possible method of generalization to systems with arbitrary number of states. The principal aim of this article is to shed light upon the method of construction of these distributions, taking into consideration their application to some experiments, and discussing their positive and negative aspects

  18. Some remarks on Feynman rules for non-commutative gauge theories based on groups G≠U(N)

    International Nuclear Information System (INIS)

    Dorn, Harald; Sieg, Christoph

    2002-01-01

    We study for subgroups G is a subset of U(N) partial summations of the θ-expanded perturbation theory. On diagrammatic level a summation procedure is established, which in the U(N) case delivers the full star-product induced rules. Thereby we uncover a cancellation mechanism between certain diagrams, which is crucial in the U(N) case, but set out of work for G is a subset of U(N). In addition, an explicit proof is given that for G is a subset of U(N), G≠U(M), M< N there is no partial summation of the θ-expanded rules resulting in new Feynman rules using the U(N) star-product vertices and besides suitable modified propagators at most a finite number of additional building blocks. Finally, we show that certain SO(N) Feynman rules conjectured in the literature cannot be derived from the enveloping algebra approach. (author)

  19. Infrared finite ghost propagator in the Feynman gauge

    International Nuclear Information System (INIS)

    Aguilar, A. C.; Papavassiliou, J.

    2008-01-01

    We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the nonperturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes nontrivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined

  20. Calculations in the Wheeler-Feynman absorber theory of radiation

    International Nuclear Information System (INIS)

    Balaji, K.S.

    1986-01-01

    One dimensional computer aided calculations were done to find the self consistent solutions for various absorber configurations in the context of the Wheeler-Feynman absorber theory, wherein every accelerating charge is assumed to produce a time symmetric combination of advanced and retarded fields. These calculations picked out the so called outerface solution for incomplete absorbers and showed that advanced as well as retarded signals interact with matter in the same manner as in the full retarded theory. Based on these calculations, the Partridge experiment and the Schmidt-Newman experiment were ruled out as tests of the absorber theory. An experiment designed to produce and detect advanced effects is proposed, based on more one-dimensional calculations

  1. Functional integral and the Feynman-Kac formula in superspace

    International Nuclear Information System (INIS)

    Ktitarev, D.V.

    1989-01-01

    We consider the Cauchy problem for linear pseudodifferential equations in superspace. The solution is constructed in the form of series. It may be regarded as a definition of a chronological exponent of a pseudodifferential operator symbol and interpreted as a functional integral in superspace. (orig.)

  2. Homological Perturbation Theory for Nonperturbative Integrals

    Science.gov (United States)

    Johnson-Freyd, Theo

    2015-11-01

    We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.

  3. Modified Feynman ratchet with velocity-dependent fluctuations

    Directory of Open Access Journals (Sweden)

    Jack Denur

    2004-03-01

    Full Text Available Abstract: The randomness of Brownian motion at thermodynamic equilibrium can be spontaneously broken by velocity-dependence of fluctuations, i.e., by dependence of values or probability distributions of fluctuating properties on Brownian-motional velocity. Such randomness-breaking can spontaneously obtain via interaction between Brownian-motional Doppler effects --- which manifest the required velocity-dependence --- and system geometrical asymmetry. A non random walk is thereby spontaneously superposed on Brownian motion, resulting in a systematic net drift velocity despite thermodynamic equilibrium. The time evolution of this systematic net drift velocity --- and of velocity probability density, force, and power output --- is derived for a velocity-dependent modification of Feynman's ratchet. We show that said spontaneous randomness-breaking, and consequent systematic net drift velocity, imply: bias from the Maxwellian of the system's velocity probability density, the force that tends to accelerate it, and its power output. Maximization, especially of power output, is discussed. Uncompensated decreases in total entropy, challenging the second law of thermodynamics, are thereby implied.

  4. Differential equations for loop integrals in Baikov representation

    Science.gov (United States)

    Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

    2018-05-01

    We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

  5. Non-negative Feynman endash Kac kernels in Schroedinger close-quote s interpolation problem

    International Nuclear Information System (INIS)

    Blanchard, P.; Garbaczewski, P.; Olkiewicz, R.

    1997-01-01

    The local formulations of the Markovian interpolating dynamics, which is constrained by the prescribed input-output statistics data, usually utilize strictly positive Feynman endash Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We discuss an extension of the framework to encompass singular potentials and associated non-negative Feynman endash Kac-type kernels. It allows us to deal with a class of continuous interpolations admitted by general non-negative solutions of the Schroedinger boundary data problem. The resulting nonstationary stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution, also away from the spatial boundaries. This observation conforms with the general mathematical theory (due to M. Nagasawa and R. Aebi) that is based on the notion of multiplicative functionals, extending in turn the well known Doob close-quote s h-transformation technique. In view of emphasizing the role of the theory of non-negative solutions of parabolic partial differential equations and the link with open-quotes Wiener exclusionclose quotes techniques used to evaluate certain Wiener functionals, we give an alternative insight into the issue, that opens a transparent route towards applications.copyright 1997 American Institute of Physics

  6. Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem

    Science.gov (United States)

    Castro, E.

    2018-02-01

    From the perturbative expansion of the exact Green function, an exact counting formula is derived to determine the number of different types of connected Feynman diagrams. This formula coincides with the Arquès-Walsh sequence formula in the rooted map theory, supporting the topological connection between Feynman diagrams and rooted maps. A classificatory summing-terms approach is used, in connection to discrete mathematical theory.

  7. Covariant path integrals on hyperbolic surfaces

    International Nuclear Information System (INIS)

    Schaefer, J.

    1997-01-01

    DeWitt close-quote s covariant formulation of path integration [B. De Witt, open-quotes Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,close quotes Rev. Mod. Phys. 29, 377 endash 397 (1957)] has two practical advantages over the traditional methods of open-quotes lattice approximations;close quotes there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature -1. The Pauli endash DeWitt curvature correction term arises, as in DeWitt close-quote s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman endash Kac formula for the automorphic Schroedinger equation on the Riemann surface Γ backslash H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47 endash 90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, open-quotes The path integral on the Poincare upper half plane and for Liouville quantum mechanics,close quotes Phys. Lett. A 123, 319 endash 328 (1987). copyright 1997 American Institute of Physics

  8. Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

    Science.gov (United States)

    Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

    2018-06-01

    We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure mathematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals, and we develop a formalism that enables us to compute these Feynman integrals in terms of our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

  9. On the coordinate (in)dependence of the formal path integral

    DEFF Research Database (Denmark)

    Johnson-Freyd, Theo

    . In this short note, aimed primarily at mathematicians, we first briefly recall the notions of Lagrangian classical and quantum field theory and the standard coordinate-full definition of the “formal” or “Feynman-diagrammatic” path integral construction. We then outline a proof of the following claim: the formal...

  10. Potential theory, path integrals and the Laplacian of the indicator

    NARCIS (Netherlands)

    R.-J. Lange (Rutger-Jan)

    2012-01-01

    markdownabstractThis paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the some seemingly ill-defined potential. The Laplacian of the indicator can be interpreted using the

  11. Quantum mechanics on the half-line using path integrals

    International Nuclear Information System (INIS)

    Clark, T.E.; Menikoff, R.; Sharp, D.H.

    1980-01-01

    We study the Feynman path-integral formalism for the constrained problem of a free particle moving on the half-line. It is shown that the effect of the boundary condition at the origin can be incorporated into the path integral by a simple modification of the action. The small-time behavior of the Green's function can be obtained from the stationary-phase evaluation of our expression for the path integral, which in this case includes contributions from both the direct and reflected classical paths

  12. One of the many visiting theoreticians, R P Feynman, who gave lectures at CERN during the year

    CERN Multimedia

    CERN PhotoLab

    1970-01-01

    Visiting CERN in January was R P Feynman, who has recently been working on strong interaction theory. On 8 January, he packed the lecture theatre, as usual, when he gave a talk on inelastic hadron collisions and is here caught in a typically graphic pose.

  13. Efficient sequential and parallel algorithms for record linkage.

    Science.gov (United States)

    Mamun, Abdullah-Al; Mi, Tian; Aseltine, Robert; Rajasekaran, Sanguthevar

    2014-01-01

    Integrating data from multiple sources is a crucial and challenging problem. Even though there exist numerous algorithms for record linkage or deduplication, they suffer from either large time needs or restrictions on the number of datasets that they can integrate. In this paper we report efficient sequential and parallel algorithms for record linkage which handle any number of datasets and outperform previous algorithms. Our algorithms employ hierarchical clustering algorithms as the basis. A key idea that we use is radix sorting on certain attributes to eliminate identical records before any further processing. Another novel idea is to form a graph that links similar records and find the connected components. Our sequential and parallel algorithms have been tested on a real dataset of 1,083,878 records and synthetic datasets ranging in size from 50,000 to 9,000,000 records. Our sequential algorithm runs at least two times faster, for any dataset, than the previous best-known algorithm, the two-phase algorithm using faster computation of the edit distance (TPA (FCED)). The speedups obtained by our parallel algorithm are almost linear. For example, we get a speedup of 7.5 with 8 cores (residing in a single node), 14.1 with 16 cores (residing in two nodes), and 26.4 with 32 cores (residing in four nodes). We have compared the performance of our sequential algorithm with TPA (FCED) and found that our algorithm outperforms the previous one. The accuracy is the same as that of this previous best-known algorithm.

  14. Feynman-Hellmann theorem for resonances and the quest for QCD exotica

    Energy Technology Data Exchange (ETDEWEB)

    Ruiz de Elvira, J. [University of Bern, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Meissner, U.G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen-und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Juelich Center for Hadron Physics and JARA-HPC, Forschungszentrum Juelich, Institute for Advanced Simulation (IAS-4), Institut fuer Kernphysik (IKP-3), Juelich (Germany); Rusetsky, A. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen-und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Schierholz, G. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany)

    2017-10-15

    The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in chiral perturbation theory and by large-N{sub c} arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible. (orig.)

  15. Theoretical confirmation of Feynman's hypothesis on the creation of circular vortices in Bose-Einstein condensates: II

    Energy Technology Data Exchange (ETDEWEB)

    Senatorski, A; Infeld, E [Soltan Institute for Nuclear Studies, Hoza 69, 00-681 Warsaw (Poland)

    2004-09-15

    In a recent paper (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865) we confirmed Feynman's hypothesis on how circular vortices can be created from an oppositely polarized linear pair in a Bose-Einstein condensate. This was done by perturbing the original pair numerically, so that a circular vortex (or array of identical circular vortices) was created as a result of reconnection. These circular vortices were then checked against known theoretical relations binding velocities and radii. Agreement to a high degree of accuracy was found. Here in part II, we give examples of the creation of several different vortices from one linear pair. All are checked as above. We also confirm the limit of separation of the line vortices below which mutual attraction, followed by annihilation, prevents the Feynman metamorphosis. Other possible modes of behaviour are illustrated.

  16. An algorithm to construct Groebner bases for solving integration by parts relations

    International Nuclear Information System (INIS)

    Smirnov, Alexander V.

    2006-01-01

    This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used to calculate Feynman integrals and has proved to be efficient in several complicated cases

  17. Integrals over products of distributions and coordinate independence of zero-temperature path integrals

    International Nuclear Information System (INIS)

    Kleinert, H.; Chervyakov, A.

    2003-01-01

    In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac δ-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in 1-ε dimensions. Our rules yield the same results as the much more cumbersome calculations in 1-ε dimensions where the limit ε→0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval

  18. A new look at the Feynman ‘hodograph’ approach to the Kepler first law

    Science.gov (United States)

    Cariñena, José F.; Rañada, Manuel F.; Santander, Mariano

    2016-03-01

    Hodographs for the Kepler problem are circles. This fact, known for almost two centuries, still provides the simplest path to derive the Kepler first law. Through Feynman’s ‘lost lecture’, this derivation has now reached a wider audience. Here we look again at Feynman’s approach to this problem, as well as the recently suggested modification by van Haandel and Heckman (vHH), with two aims in mind, both of which extend the scope of the approach. First we review the geometric constructions of the Feynman and vHH approaches (that prove the existence of elliptic orbits without making use of integral calculus or differential equations) and then extend the geometric approach to also cover the hyperbolic orbits (corresponding to E\\gt 0). In the second part we analyse the properties of the director circles of the conics, which are used to simplify the approach, and we relate with the properties of the hodographs and Laplace-Runge-Lenz vector the constant of motion specific to the Kepler problem. Finally, we briefly discuss the generalisation of the geometric method to the Kepler problem in configuration spaces of constant curvature, i.e. in the sphere and the hyperbolic plane.

  19. Multimodal sensory integration during sequential eating--linking chewing activity, aroma release, and aroma perception over time.

    Science.gov (United States)

    Leclercq, Ségolène; Blancher, Guillaume

    2012-10-01

    The respective effects of chewing activity, aroma release from a gelled candy, and aroma perception were investigated. Specifically, the study aimed at 1) comparing an imposed chewing and swallowing pattern (IP) and free protocol (FP) on panelists for in vivo measurements, 2) investigating carryover effects in sequential eating, and 3) studying the link between instrumental data and their perception counterpart. Chewing activity, in-nose aroma concentration, and aroma perception over time were measured by electromyography, proton transfer reaction-mass spectrometry, and time intensity, respectively. Model gel candies were flavored at 2 intensity levels (low-L and high-H). The panelists evaluated 3 sequences (H then H, H then L, and L then H) in duplicates with both IP and FP. They scored aroma intensity over time while their in-nose aroma concentrations and their chewing activity were measured. Overall, only limited advantages were found in imposing a chewing and swallowing pattern for instrumental and sensory data. In addition, the study highlighted the role of brain integration on perceived intensity and dynamics of perception, in the framework of sequential eating without rinsing. Because of the presence of adaptation phenomena, contrast effect, and potential taste and texture cross-modal interaction with aroma perception, it was concluded that dynamic in-nose concentration data provide only one part of the perception picture and therefore cannot be used alone in prediction models.

  20. Functional Integration

    Science.gov (United States)

    Cartier, Pierre; DeWitt-Morette, Cecile

    2010-06-01

    Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

  1. Analytic results for planar three-loop integrals for massive form factors

    Energy Technology Data Exchange (ETDEWEB)

    Henn, Johannes M. [PRISMA Cluster of Excellence, Johannes Gutenberg Universität Mainz,55099 Mainz (Germany); Kavli Institute for Theoretical Physics, UC Santa Barbara,Santa Barbara (United States); Smirnov, Alexander V. [Research Computing Center, Moscow State University,119992 Moscow (Russian Federation); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics of Moscow State University,119992 Moscow (Russian Federation); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT),76128 Karlsruhe (Germany)

    2016-12-28

    We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general q{sup 2} are expressed in terms of multiple polylogarithms, and results for fiftyone master integrals at the threshold q{sup 2}=4m{sup 2} are expressed in terms of multiple polylogarithms of argument one, with indices equal to zero or to a sixth root of unity.

  2. MPL-A program for computations with iterated integrals on moduli spaces of curves of genus zero

    Science.gov (United States)

    Bogner, Christian

    2016-06-01

    We introduce the Maple program MPL for computations with multiple polylogarithms. The program is based on homotopy invariant iterated integrals on moduli spaces M0,n of curves of genus 0 with n ordered marked points. It includes the symbol map and procedures for the analytic computation of period integrals on M0,n. It supports the automated computation of a certain class of Feynman integrals.

  3. Path integral solution of the Dirichlet problem

    International Nuclear Information System (INIS)

    LaChapelle, J.

    1997-01-01

    A scheme for functional integration developed by Cartier/DeWitt-Morette is first reviewed and then employed to construct the path integral representation for the solution of the Dirichlet problem in terms of first exit time. The path integral solution is then applied to calculate the fixed-energy point-to-point transition amplitude both in configuration and phase space. The path integral solution can also be derived using physical principles based on Feynman close-quote s original reasoning. We check that the Fourier transform in energy of the fixed-energy point-to-point transition amplitude gives the well known time-dependent transition amplitude, and calculate the WKB approximation. copyright 1997 Academic Press, Inc

  4. Adaptive control in multi-threaded iterated integration

    International Nuclear Information System (INIS)

    Doncker, Elise de; Yuasa, Fukuko

    2013-01-01

    In recent years we have developed a technique for the direct computation of Feynman loop-integrals, which are notorious for the occurrence of integrand singularities. Especially for handling singularities in the interior of the domain, we approximate the iterated integral using an adaptive algorithm in the coordinate directions. We present a novel multi-core parallelization scheme for adaptive multivariate integration, by assigning threads to the rule evaluations in the outer dimensions of the iterated integral. The method ensures a large parallel granularity as each function evaluation by itself comprises an integral over the lower dimensions, while the application of the threads is governed by the adaptive control in the outer level. We give computational results for a test set of 3- to 6-dimensional integrals, where several problems exhibit a loop integral behavior.

  5. Self-consistence equations for extended Feynman rules in quantum chromodynamics

    International Nuclear Information System (INIS)

    Wielenberg, A.

    2005-01-01

    In this thesis improved solutions for Green's functions are obtained. First the for this thesis essential techniques and concepts of QCD as euclidean field theory are presented. After a discussion of the foundations of the extended approach for the Feynman rules of QCD with a systematic approach for the 4-gluon vertex a modified renormalization scheme for the extended approach is developed. Thereafter the resummation of the Dyson-Schwinger equations (DSE) by the appropriately modified Bethe-Salpeter equation is discussed. Then the leading divergences for the 1-loop graphs of the resummed DSE are determined. Thereafter the equation-of-motion condensate is defined as result of an operator-product expansion. Then the self-consistency equations for the extended approaches are defined and numerically solved. (HSI)

  6. Tight connexion between the Einstein-Podolsky-Rosen non-separability and the non-locality in Feynman's theory of antiparticles

    International Nuclear Information System (INIS)

    Costa de Beauregard, Olivier

    1976-01-01

    The Feynman amplitude for the annihilation transition of an electron-positon pair contains the two polarization correlations of the photons respectively characterizing the 0-1-0 and 1-1-0 cascades. The overall system is in general neither P- nor C-, but is PC-invariant [fr

  7. Properties of the Feynman-alpha method applied to accelerator-driven subcritical systems.

    Science.gov (United States)

    Taczanowski, S; Domanska, G; Kopec, M; Janczyszyn, J

    2005-01-01

    A Monte Carlo study of the Feynman-method with a simple code simulating the multiplication chain, confined to pertinent time-dependent phenomena has been done. The significance of its key parameters (detector efficiency and dead time, k-source and spallation neutrons multiplicities, required number of fissions etc.) has been discussed. It has been demonstrated that this method can be insensitive to properties of the zones surrounding the core, whereas is strongly affected by the detector dead time. In turn, the influence of harmonics in the neutron field and of the dispersion of spallation neutrons has proven much less pronounced.

  8. Sequential circuit design for radiation hardened multiple voltage integrated circuits

    Science.gov (United States)

    Clark, Lawrence T [Phoenix, AZ; McIver, III, John K.

    2009-11-24

    The present invention includes a radiation hardened sequential circuit, such as a bistable circuit, flip-flop or other suitable design that presents substantial immunity to ionizing radiation while simultaneously maintaining a low operating voltage. In one embodiment, the circuit includes a plurality of logic elements that operate on relatively low voltage, and a master and slave latches each having storage elements that operate on a relatively high voltage.

  9. Absolute measurement of β eff based on Feynman-α experiments and the two-region model in the IPEN/MB-01 research reactor

    International Nuclear Information System (INIS)

    Kuramoto, Renato Y.R.; Santos, Adimir dos; Jerez, Rogerio; Diniz, Ricardo

    2007-01-01

    A new methodology for absolute measurement of the effective delayed neutron fraction β eff based on Feynman-α experiments and the two-region model was developed. This method made use of Feynman-α experiments and the two-region model. To examine the present methodology, a series of Feynman-α experiments were conducted at the IPEN/MB-01 research reactor facility. In contrast with other techniques like the slope method, Nelson-number method and 252 Cf-source method, the main advantage of this new methodology is to obtain β eff with the required accuracy and without knowledge of any other parameter. By adopting the present approach, β eff was measured with a 0.67% uncertainty. In addition, the prompt neutron generation time, Λ, and other parameters, was also obtained in an absolute experimental way. In general, the measured parameters are in good agreement with the values found from frequency analysis experiments. The theory-experiment comparison for the β eff measured in this work shows that JENDL3.3 presented the best agreement (within 1%). The reduction of the 235 U thermal yield as proposed by Okajima and Sakurai is completely justified according to the β eff measurements performed in this work

  10. Path integral theory and deep inelastic scattering of nuclei

    International Nuclear Information System (INIS)

    Neto, J.L.

    1981-10-01

    A formalism, based on Feynman's path integral, is developed and used in the theory of deep inelastic collisions of nuclei. Having shown how to express the propagator of the Wigner function of an isolated system as a (double) path integral in phase space, random processes are considered and the influence functional in interacting systems is discussed. A semi-classical description for the reduced Wigner and a generalized Langevin equation are given. Finally, the formalism is used in a random matrix model for deep inelastic collisions. (U.K.)

  11. Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group

    International Nuclear Information System (INIS)

    Morariu, B.

    1997-01-01

    The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin

  12. Measurement of Feynman-x spectra of photons and neutrons in the very forward direction in deep-inelastic scattering at HERA

    International Nuclear Information System (INIS)

    Andreev, V.; Baghdasaryan, A.; Begzsuren, K.

    2014-03-01

    Measurements of normalised cross sections for the production of photons and neutrons at very small angles with respect to the proton beam direction in deep-inelastic ep scattering at HERA are presented as a function of the Feynman variable x F and of the centre-of-mass energy of the virtual photon-proton system W. The data are taken with the H1 detector in the years 2006 and 2007 and correspond to an integrated luminosity of 131 pb -1 . The measurement is restricted to photons and neutrons in the pseudorapidity range η > 7.9 and covers the range of negative four momentum transfer squared at the positron vertex 6 2 2 , of inelasticity 0.05 F dependent cross sections is investigated. Predictions of deep-inelastic scattering models and of models for hadronic interactions of high energy cosmic rays are compared to the measured cross sections.

  13. Comparison of MCNP6 and experimental results for neutron counts, Rossi-α, and Feynman-α distributions

    International Nuclear Information System (INIS)

    Talamo, A.; Gohar, Y.; Sadovich, S.; Kiyavitskaya, H.; Bournos, V.; Fokov, Y.; Routkovskaya, C.

    2013-01-01

    MCNP6, the general-purpose Monte Carlo N-Particle code, has the capability to perform time-dependent calculations by tracking the time interval between successive events of the neutron random walk. In fixed-source calculations for a subcritical assembly, the zero time value is assigned at the moment the neutron is emitted by the external neutron source. The PTRAC and F8 cards of MCNP allow to tally the time when a neutron is captured by 3 He(n, p) reactions in the neutron detector. From this information, it is possible to build three different time distributions: neutron counts, Rossi-α, and Feynman-α. The neutron counts time distribution represents the number of neutrons captured as a function of time. The Rossi-a distribution represents the number of neutron pairs captured as a function of the time interval between two capture events. The Feynman-a distribution represents the variance-to-mean ratio, minus one, of the neutron counts array as a function of a fixed time interval. The MCNP6 results for these three time distributions have been compared with the experimental data of the YALINA Thermal facility and have been found to be in quite good agreement. (authors)

  14. Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms

    Science.gov (United States)

    Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus; von Hippel, Matt; Wilhelm, Matthias

    2018-03-01

    We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.

  15. Mean-Variance-Validation Technique for Sequential Kriging Metamodels

    International Nuclear Information System (INIS)

    Lee, Tae Hee; Kim, Ho Sung

    2010-01-01

    The rigorous validation of the accuracy of metamodels is an important topic in research on metamodel techniques. Although a leave-k-out cross-validation technique involves a considerably high computational cost, it cannot be used to measure the fidelity of metamodels. Recently, the mean 0 validation technique has been proposed to quantitatively determine the accuracy of metamodels. However, the use of mean 0 validation criterion may lead to premature termination of a sampling process even if the kriging model is inaccurate. In this study, we propose a new validation technique based on the mean and variance of the response evaluated when sequential sampling method, such as maximum entropy sampling, is used. The proposed validation technique is more efficient and accurate than the leave-k-out cross-validation technique, because instead of performing numerical integration, the kriging model is explicitly integrated to accurately evaluate the mean and variance of the response evaluated. The error in the proposed validation technique resembles a root mean squared error, thus it can be used to determine a stop criterion for sequential sampling of metamodels

  16. Sequential Power-Dependence Theory

    NARCIS (Netherlands)

    Buskens, Vincent; Rijt, Arnout van de

    2008-01-01

    Existing methods for predicting resource divisions in laboratory exchange networks do not take into account the sequential nature of the experimental setting. We extend network exchange theory by considering sequential exchange. We prove that Sequential Power-Dependence Theory—unlike

  17. Abelian Chern endash Simons theory. II. A functional integral approach

    International Nuclear Information System (INIS)

    Manoliu, M.

    1998-01-01

    Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics

  18. On some mathematical problems in the definition of Feynman path integral

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Sirugue-Collin, M.

    1976-07-01

    It is shown how integration on a Hilbert space of paths can be performed to get exact evolution of non relativistic quantum systems for a rather large class of potentials including polynomial interaction

  19. Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

    KAUST Repository

    Zuberi, M. A. H.; Alkhalifah, Tariq Ali

    2014-01-01

    Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

  20. Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

    KAUST Repository

    Zuberi, M. A. H.

    2014-05-19

    Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

  1. Gravitational lensing of the CMB: A Feynman diagram approach

    Directory of Open Access Journals (Sweden)

    Elizabeth E. Jenkins

    2014-09-01

    Full Text Available We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS. We study the Hu–Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to O(ϕ4 in the lensing potential ϕ. By identifying the diagrams responsible for the previously noted large O(ϕ4 term, we conclude that the lensing expansion does not break down. The convergence can be significantly improved by a reorganization of the ϕ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel, including many previously unexplored cases. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields.

  2. Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Raab, Clemens G.

    2014-07-01

    Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.

  3. Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2014-07-15

    Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.

  4. The two-loop master integrals for qq-bar→VV

    International Nuclear Information System (INIS)

    Gehrmann, Thomas; Manteuffel, Andreas von; Tancredi, Lorenzo; Weihs, Erich

    2014-01-01

    We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, qq-bar→VV, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion

  5. The Feynman lectures on physics

    International Nuclear Information System (INIS)

    Feynman, R.P.

    1979-01-01

    This set of lectures tries to elucidate from the beginning those features of the quantum mechanics which are most general. The first lectures tackle head on the ideas of a probability amplitude, the interference of amplitudes, the abstract notion of a state, and the superposition and resolution of states - and the Dirac notation is used from the start. In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible. The time dependence of states including states of definite energy comes next, and the ideas are applied at once to the study of two-state systems. A detailed discussion of the ammonia maser provides the framework for the introduction to radiation absorption and induced transitions. The lectures then go on to consider more complex systems, leading to a discussion of the propagation of electrons in a crystal, and to a rather complete treatment of the quantum mechanics of angular momentum. Our introduction to quantum mechanics ends in Chapter 20 with a discussion of the Schroedinger wave function, its differential equation, and the solution for the hydrogen atom. The last Chapter of this volume is not intended to be a part of the 'course.' It is a 'seminar' on superconductivity and was given in the spirit of some of the entertainment lectures of the first two volumes, with the intent of opening to the students a broader view of the relation of what they were learning to the general culture of physics. Feynman's 'epilogue' serves as the period to the three-volume series [fr

  6. Comparison of MCNP6 and experimental results for neutron counts, Rossi-{alpha}, and Feynman-{alpha} distributions

    Energy Technology Data Exchange (ETDEWEB)

    Talamo, A.; Gohar, Y. [Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439 (United States); Sadovich, S.; Kiyavitskaya, H.; Bournos, V.; Fokov, Y.; Routkovskaya, C. [Joint Institute for Power and Nuclear Research-Sosny, 99 Academician A.K. Krasin Str., Minsk 220109 (Belarus)

    2013-07-01

    MCNP6, the general-purpose Monte Carlo N-Particle code, has the capability to perform time-dependent calculations by tracking the time interval between successive events of the neutron random walk. In fixed-source calculations for a subcritical assembly, the zero time value is assigned at the moment the neutron is emitted by the external neutron source. The PTRAC and F8 cards of MCNP allow to tally the time when a neutron is captured by {sup 3}He(n, p) reactions in the neutron detector. From this information, it is possible to build three different time distributions: neutron counts, Rossi-{alpha}, and Feynman-{alpha}. The neutron counts time distribution represents the number of neutrons captured as a function of time. The Rossi-a distribution represents the number of neutron pairs captured as a function of the time interval between two capture events. The Feynman-a distribution represents the variance-to-mean ratio, minus one, of the neutron counts array as a function of a fixed time interval. The MCNP6 results for these three time distributions have been compared with the experimental data of the YALINA Thermal facility and have been found to be in quite good agreement. (authors)

  7. Path integrals in quantum mechanics, statistics, polymer physics, and financial markets

    CERN Document Server

    Kleinert, Hagen

    2009-01-01

    This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p

  8. Computer algebra in quantum field theory integration, summation and special functions

    CERN Document Server

    Schneider, Carsten

    2013-01-01

    The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including

  9. Multidimensional oriented solid-state NMR experiments enable the sequential assignment of uniformly 15N labeled integral membrane proteins in magnetically aligned lipid bilayers

    International Nuclear Information System (INIS)

    Mote, Kaustubh R.; Gopinath, T.; Traaseth, Nathaniel J.; Kitchen, Jason; Gor’kov, Peter L.; Brey, William W.; Veglia, Gianluigi

    2011-01-01

    Oriented solid-state NMR is the most direct methodology to obtain the orientation of membrane proteins with respect to the lipid bilayer. The method consists of measuring 1 H- 15 N dipolar couplings (DC) and 15 N anisotropic chemical shifts (CSA) for membrane proteins that are uniformly aligned with respect to the membrane bilayer. A significant advantage of this approach is that tilt and azimuthal (rotational) angles of the protein domains can be directly derived from analytical expression of DC and CSA values, or, alternatively, obtained by refining protein structures using these values as harmonic restraints in simulated annealing calculations. The Achilles’ heel of this approach is the lack of suitable experiments for sequential assignment of the amide resonances. In this Article, we present a new pulse sequence that integrates proton driven spin diffusion (PDSD) with sensitivity-enhanced PISEMA in a 3D experiment ([ 1 H, 15 N]-SE-PISEMA-PDSD). The incorporation of 2D 15 N/ 15 N spin diffusion experiments into this new 3D experiment leads to the complete and unambiguous assignment of the 15 N resonances. The feasibility of this approach is demonstrated for the membrane protein sarcolipin reconstituted in magnetically aligned lipid bicelles. Taken with low electric field probe technology, this approach will propel the determination of sequential assignment as well as structure and topology of larger integral membrane proteins in aligned lipid bilayers.

  10. Cortical responses following simultaneous and sequential retinal neurostimulation with different return configurations.

    Science.gov (United States)

    Barriga-Rivera, Alejandro; Morley, John W; Lovell, Nigel H; Suaning, Gregg J

    2016-08-01

    Researchers continue to develop visual prostheses towards safer and more efficacious systems. However limitations still exist in the number of stimulating channels that can be integrated. Therefore there is a need for spatial and time multiplexing techniques to provide improved performance of the current technology. In particular, bright and high-contrast visual scenes may require simultaneous activation of several electrodes. In this research, a 24-electrode array was suprachoroidally implanted in three normally-sighted cats. Multi-unit activity was recorded from the primary visual cortex. Four stimulation strategies were contrasted to provide activation of seven electrodes arranged hexagonally: simultaneous monopolar, sequential monopolar, sequential bipolar and hexapolar. Both monopolar configurations showed similar cortical activation maps. Hexapolar and sequential bipolar configurations activated a lower number of cortical channels. Overall, the return configuration played a more relevant role in cortical activation than time multiplexing and thus, rapid sequential stimulation may assist in reducing the number of channels required to activate large retinal areas.

  11. Path integrals for inertialess classical particles under-going rapid stochastic trembling. I

    International Nuclear Information System (INIS)

    Bezak, V.

    1978-01-01

    Feynman path integrals are studied in reference to the Fokker-Planck (Smoluchowski) equation. Examples are presented including the motion of an inertialess classical charged particle between electrodes in plate and cylindrical capacitors with charges fluctuating rapidly as Gaussian white-noise stochastic processes. Another example concerns magnetodiffusion of a charged particle in an non-polarized electromagnetic beam characterized by a white-noise spectrum. (author)

  12. Application of path integral method to heavy ion reactions, 1. General formalism

    Energy Technology Data Exchange (ETDEWEB)

    Fujita, J; Negishi, T [Tokyo Univ. of Education (Japan). Dept. of Physics

    1976-03-01

    The semiclassical approach for heavy ion reactions has become more and more important in analyzing rapidly accumulating data. The purpose of this paper is to lay a quantum-mechanical foundation of the conventional semiclassical treatments in heavy ion physics by using Feynman's path integral method on the basis of the second paper of Pechukas, and discuss simple consequences of the formalism.

  13. Developing a Self-Report-Based Sequential Analysis Method for Educational Technology Systems: A Process-Based Usability Evaluation

    Science.gov (United States)

    Lin, Yi-Chun; Hsieh, Ya-Hui; Hou, Huei-Tse

    2015-01-01

    The development of a usability evaluation method for educational systems or applications, called the self-report-based sequential analysis, is described herein. The method aims to extend the current practice by proposing self-report-based sequential analysis as a new usability method, which integrates the advantages of self-report in survey…

  14. Leading singularities and off-shell conformal integrals

    CERN Document Server

    Drummond, James; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.

    2013-01-01

    The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol - with an appropriate ansatz for its structure - as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the ...

  15. One-loop tensor integrals in dimensional regularisation

    International Nuclear Information System (INIS)

    Campbell, J.M.; Glover, E.W.N.; Miller, D.J.

    1997-01-01

    We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of n- and (n-1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to the external parameters - essentially yielding scalar integrals with Feynman parameters in the numerator - or by developing the scalar integral in D=6-2ε or higher dimensions. An additional advantage is that other spurious kinematic singularities are also controlled. As an explicit example, we develop the tensor integrals and associated scalar integral combinations for processes where the internal particles are massless and where up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals. (orig.)

  16. Temporal integration of sequential auditory events: silent period in sound pattern activates human planum temporale.

    Science.gov (United States)

    Mustovic, Henrietta; Scheffler, Klaus; Di Salle, Francesco; Esposito, Fabrizio; Neuhoff, John G; Hennig, Jürgen; Seifritz, Erich

    2003-09-01

    Temporal integration is a fundamental process that the brain carries out to construct coherent percepts from serial sensory events. This process critically depends on the formation of memory traces reconciling past with present events and is particularly important in the auditory domain where sensory information is received both serially and in parallel. It has been suggested that buffers for transient auditory memory traces reside in the auditory cortex. However, previous studies investigating "echoic memory" did not distinguish between brain response to novel auditory stimulus characteristics on the level of basic sound processing and a higher level involving matching of present with stored information. Here we used functional magnetic resonance imaging in combination with a regular pattern of sounds repeated every 100 ms and deviant interspersed stimuli of 100-ms duration, which were either brief presentations of louder sounds or brief periods of silence, to probe the formation of auditory memory traces. To avoid interaction with scanner noise, the auditory stimulation sequence was implemented into the image acquisition scheme. Compared to increased loudness events, silent periods produced specific neural activation in the right planum temporale and temporoparietal junction. Our findings suggest that this area posterior to the auditory cortex plays a critical role in integrating sequential auditory events and is involved in the formation of short-term auditory memory traces. This function of the planum temporale appears to be fundamental in the segregation of simultaneous sound sources.

  17. Programme for test generation for combinatorial and sequential systems

    International Nuclear Information System (INIS)

    Tran Huy Hoan

    1973-01-01

    This research thesis reports the computer-assisted search for tests aimed at failure detection in combinatorial and sequential logic circuits. As he wants to deal with complex circuits with many modules such as those met in large scale integrated circuits (LSI), the author used propagation paths. He reports the development of a method which is valid for combinatorial systems and for several sequential circuits comprising elementary logic modules and JK and RS flip-flops. This method is developed on an IBM 360/91 computer in PL/1 language. The used memory space is limited and adjustable with respect to circuit dimension. Computing time is short when compared to that needed by other programmes. The solution is practical and efficient for failure test and localisation

  18. Critical exponents predicted by grouping of Feynman diagrams in φ4 model

    International Nuclear Information System (INIS)

    Kaupuzs, J.

    2001-01-01

    Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments. (orig.)

  19. Generalized conditions for the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space

    International Nuclear Information System (INIS)

    Manoukian, E.B.

    1986-01-01

    Generalized conditions (rules) are set up for the existence of the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space. These rules are generalizations of rules that have been set up earlier by us and hence are applicable to a larger class of graphs. The study is very general as the vanishing masses are led to vanish at different rates. All subtractions of renormalization are carried out directly in momentum space, about the origin, with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram

  20. POLYP: an automatic device for drawing sequential samples of gas

    Energy Technology Data Exchange (ETDEWEB)

    Gaglione, P; Koechler, C; Stanchi, L

    1974-12-01

    Polyp is an automatic device consisting of electronic equipment which drives sequentially 8 small pumps for drawing samples of gas. The electronic circuit is driven by a quartz oscillator and allows for the preselection of a waiting time in such a manner that a set of similar instruments placed in suitable position in the open country will start simultaneously. At the same time the first pump of each instrument will inflate a plastic bag for a preset time. The other seven pumps will inflate sequentially the other bags. The instrument is powered by rechargeable batteries and realized with C-MUS integrated circuits for a nearly negligible consumption. As it is foreseen for field operation it is waterproof.

  1. POLYP: an automatic device for drawing sequential samples of gas

    International Nuclear Information System (INIS)

    Gaglione, P.; Koechler, C.; Stanchi, L.

    1974-12-01

    POLYP is an automatic device consisting of an electronic equipment which drives sequentially 8 small pumps for drawing samples of gas. The electronic circuit is driven by a quartz oscillator and allows for the preselection of a waiting time in such a manner that a set of similar instruments placed in suitable position in the open country will start simultaneously. At the same time the first pump of each instrument will inflate a plastic bag for a preset time. Thereafter the other seven pumps will inflate sequentially the other bag. The instrument is powered by rechargeable batteries and realized with C-MOS integrated circuits for a nearly negligible consumption. As it is foreseen for field operation it is waterproof

  2. Application of FIRE for the calculation of photon matrix elements

    Indian Academy of Sciences (India)

    to evaluate the two-loop Feynman diagrams for the photon matrix element of the ... sum of scalar Feynman integrals to a linear combination of a few master integrals. .... Then, FIRE is used to express these scalar integrals as a linear combi-.

  3. Multidimensional oriented solid-state NMR experiments enable the sequential assignment of uniformly 15N labeled integral membrane proteins in magnetically aligned lipid bilayers.

    Science.gov (United States)

    Mote, Kaustubh R; Gopinath, T; Traaseth, Nathaniel J; Kitchen, Jason; Gor'kov, Peter L; Brey, William W; Veglia, Gianluigi

    2011-11-01

    Oriented solid-state NMR is the most direct methodology to obtain the orientation of membrane proteins with respect to the lipid bilayer. The method consists of measuring (1)H-(15)N dipolar couplings (DC) and (15)N anisotropic chemical shifts (CSA) for membrane proteins that are uniformly aligned with respect to the membrane bilayer. A significant advantage of this approach is that tilt and azimuthal (rotational) angles of the protein domains can be directly derived from analytical expression of DC and CSA values, or, alternatively, obtained by refining protein structures using these values as harmonic restraints in simulated annealing calculations. The Achilles' heel of this approach is the lack of suitable experiments for sequential assignment of the amide resonances. In this Article, we present a new pulse sequence that integrates proton driven spin diffusion (PDSD) with sensitivity-enhanced PISEMA in a 3D experiment ([(1)H,(15)N]-SE-PISEMA-PDSD). The incorporation of 2D (15)N/(15)N spin diffusion experiments into this new 3D experiment leads to the complete and unambiguous assignment of the (15)N resonances. The feasibility of this approach is demonstrated for the membrane protein sarcolipin reconstituted in magnetically aligned lipid bicelles. Taken with low electric field probe technology, this approach will propel the determination of sequential assignment as well as structure and topology of larger integral membrane proteins in aligned lipid bilayers. © Springer Science+Business Media B.V. 2011

  4. Methods, safety, and early clinical outcomes of dose escalation using simultaneous integrated and sequential boosts in patients with locally advanced gynecologic malignancies.

    Science.gov (United States)

    Boyle, John; Craciunescu, Oana; Steffey, Beverly; Cai, Jing; Chino, Junzo

    2014-11-01

    To evaluate the safety of dose escalated radiotherapy using a simultaneous integrated boost technique in patients with locally advanced gynecological malignancies. Thirty-nine women with locally advanced gynecological malignancies were treated with intensity modulated radiation therapy utilizing a simultaneous integrated boost (SIB) technique for gross disease in the para-aortic and/or pelvic nodal basins, sidewall extension, or residual primary disease. Women were treated to 45Gy in 1.8Gy fractions to elective nodal regions. Gross disease was simultaneously treated to 55Gy in 2.2Gy fractions (n=44 sites). An additional sequential boost of 10Gy in 2Gy fractions was delivered if deemed appropriate (n=29 sites). Acute and late toxicity, local control in the treated volumes (LC), overall survival (OS), and distant metastases (DM) were assessed. All were treated with a SIB to a dose of 55Gy. Twenty-four patients were subsequently treated with a sequential boost to a median dose of 65Gy. Median follow-up was 18months. Rates of acute>grade 2 gastrointestinal (GI), genitourinary (GU), and hematologic (heme) toxicities were 2.5%, 0%, and 30%, respectively. There were no grade 4 acute toxicities. At one year, grade 1-2 late GI toxicities were 24.5%. There were no grade 3 or 4 late GI toxicities. Rates of grade 1-2 late GU toxicities were 12.7%. There were no grade 3 or 4 late GU toxicities. Dose escalated radiotherapy using a SIB results in acceptable rates of acute toxicity. Copyright © 2014 Elsevier Inc. All rights reserved.

  5. A fast and accurate online sequential learning algorithm for feedforward networks.

    Science.gov (United States)

    Liang, Nan-Ying; Huang, Guang-Bin; Saratchandran, P; Sundararajan, N

    2006-11-01

    In this paper, we develop an online sequential learning algorithm for single hidden layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes in a unified framework. The algorithm is referred to as online sequential extreme learning machine (OS-ELM) and can learn data one-by-one or chunk-by-chunk (a block of data) with fixed or varying chunk size. The activation functions for additive nodes in OS-ELM can be any bounded nonconstant piecewise continuous functions and the activation functions for RBF nodes can be any integrable piecewise continuous functions. In OS-ELM, the parameters of hidden nodes (the input weights and biases of additive nodes or the centers and impact factors of RBF nodes) are randomly selected and the output weights are analytically determined based on the sequentially arriving data. The algorithm uses the ideas of ELM of Huang et al. developed for batch learning which has been shown to be extremely fast with generalization performance better than other batch training methods. Apart from selecting the number of hidden nodes, no other control parameters have to be manually chosen. Detailed performance comparison of OS-ELM is done with other popular sequential learning algorithms on benchmark problems drawn from the regression, classification and time series prediction areas. The results show that the OS-ELM is faster than the other sequential algorithms and produces better generalization performance.

  6. Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

    Science.gov (United States)

    Meyer, Christoph

    2018-01-01

    The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.

  7. Alternative Evaluation of a ln tan Integral Arising in Quantum Field Theory

    International Nuclear Information System (INIS)

    Coffey, Mark W.

    2010-01-01

    A certain dilogarithmic integral I 7 turns up in a number of contexts including Feynman diagram calculations, volumes of tetrahedra in hyperbolic geometry, knot theory, and conjectured relations in analytic number theory. We provide an alternative explicit evaluation of a parameterized family of integrals containing this particular case. By invoking the Bloch-Wigner form of the dilogarithm function, we produce an equivalent result, giving a third evaluation of I 7 . We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl 2 .

  8. Modelling sequentially scored item responses

    NARCIS (Netherlands)

    Akkermans, W.

    2000-01-01

    The sequential model can be used to describe the variable resulting from a sequential scoring process. In this paper two more item response models are investigated with respect to their suitability for sequential scoring: the partial credit model and the graded response model. The investigation is

  9. Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the 'passage time' in tunneling

    International Nuclear Information System (INIS)

    Garcia-Calderon, Gaston; Villavicencio, Jorge; Yamada, Norifumi

    2003-01-01

    We show the equivalence of the functions G p (t) and vertical bar Ψ(d,t) vertical bar 2 for the 'passage time' in tunneling. The former, obtained within the framework of the real-time Feynman histories approach to the tunneling time problem, uses the Gell-Mann and Hartle's decoherence functional, and the latter involves an exact analytical solution to the time-dependent Schroedinger equation for cutoff initial waves

  10. Comment on 'Path integral solution for a Mie-type potential'

    International Nuclear Information System (INIS)

    Steiner, F.

    1985-01-01

    We comment on several incorrect results given in a recent paper by Erkoc and Sever (ES). In particular, it is pointed out that their path integral formula for the one-dimensional Mie-Lennard-Jones potential is wrong, since a quantum correction proportional to (h/2π) 2 - which is a consequence of the stochastic nature of the Feynman paths - has been overlooked. The correct expression can be obtained from a general path integral formula, which we have derived in a previous paper. For the particular potential discussed in detail by ES, we give a complete path integral treatment, which allows us to derive the energies and normalized wave functions of the discrete spectrum. (orig.)

  11. Calculation of quantum-mechanical system energy spectra using path integrals

    International Nuclear Information System (INIS)

    Evseev, A.M.; Dmitriev, V.P.

    1977-01-01

    A solution of the Feynman quantum-mechanical integral connecting a wave function (psi (x, t)) at a moment t+tau (tau → 0) with the wave function at the moment t is provided by complex variable substitution and subsequent path integration. Time dependence of the wave function is calculated by the Monte Carlo method. The Fourier inverse transformation of the wave function by path integration calculated has been applied to determine the energy spectra. Energy spectra are presented of a hydrogen atom derived from wave function psi (x, t) at different x, as well as boson energy spectra of He, Li, and Be atoms obtained from psi (x, t) at X = O

  12. Distributed and multi-core computation of 2-loop integrals

    International Nuclear Information System (INIS)

    De Doncker, E; Yuasa, F

    2014-01-01

    For an automatic computation of Feynman loop integrals in the physical region we rely on an extrapolation technique where the integrals of the sequence are obtained with iterated/repeated adaptive methods from the QUADPACK 1D quadrature package. The integration rule evaluations in the outer level, corresponding to independent inner integral approximations, are assigned to threads dynamically via the OpenMP runtime in the parallel implementation. Furthermore, multi-level (nested) parallelism enables an efficient utilization of hyperthreading or larger numbers of cores. For a class of loop integrals in the unphysical region, which do not suffer from singularities in the interior of the integration domain, we find that the distributed adaptive integration methods in the multivariate PARINT package are highly efficient and accurate. We apply these techniques without resorting to integral transformations and report on the capabilities of the algorithms and the parallel performance for a test set including various types of two-loop integrals

  13. Salecker-Wigner-Peres clock, Feynman paths, and a tunneling time that should not exist

    Science.gov (United States)

    Sokolovski, D.

    2017-08-01

    The Salecker-Wigner-Peres (SWP) clock is often used to determine the duration a quantum particle is supposed to spend in a specified region of space Ω . By construction, the result is a real positive number, and the method seems to avoid the difficulty of introducing complex time parameters, which arises in the Feynman paths approach. However, it tells little about the particle's motion. We investigate this matter further, and show that the SWP clock, like any other Larmor clock, correlates the rotation of its angular momentum with the durations τ , which the Feynman paths spend in Ω , thereby destroying interference between different durations. An inaccurate weakly coupled clock leaves the interference almost intact, and the need to resolve the resulting "which way?" problem is one of the main difficulties at the center of the "tunnelling time" controversy. In the absence of a probability distribution for the values of τ , the SWP results are expressed in terms of moduli of the "complex times," given by the weighted sums of the corresponding probability amplitudes. It is shown that overinterpretation of these results, by treating the SWP times as physical time intervals, leads to paradoxes and should be avoided. We also analyze various settings of the SWP clock, different calibration procedures, and the relation between the SWP results and the quantum dwell time. The cases of stationary tunneling and tunnel ionization are considered in some detail. Although our detailed analysis addresses only one particular definition of the duration of a tunneling process, it also points towards the impossibility of uniting various time parameters, which may occur in quantum theory, within the concept of a single tunnelling time.

  14. Distribution definition of path integrals

    International Nuclear Information System (INIS)

    Kerler, W.

    1979-01-01

    By starting from quantum mechanics it turns out that a rather general definition of quantum functional integrals can be given which is based on distribution theory. It applies also to curved space and provides clear rules for non-linear transformations. The refinements necessary in usual definitions of path integrals are pointed out. Since the quantum nature requires special care with time sequences, it is not the classical phase space which occurs in the phase-space form of the path integral. Feynman's configuration-space form only applies to a highly specialized situation, and therefore is not a very advantageous starting point for general investigations. It is shown that the commonly used substitutions of variables do not properly account for quantum effects. The relation to the traditional ordering problem is clarified. The distribution formulation has allowed to treat constrained systems directly at the quantum level, to complete the path integral formulation of the equivalence theorem, and to define functional integrals also for space translation after the transition to fields. (orig.)

  15. Feynman-α correlation analysis by prompt-photon detection

    International Nuclear Information System (INIS)

    Hashimoto, Kengo; Yamada, Sumasu; Hasegawa, Yasuhiro; Horiguchi, Tetsuo

    1998-01-01

    Two-detector Feynman-α measurements were carried out using the UTR-KINKI reactor, a light-water-moderated and graphite-reflected reactor, by detecting high-energy, prompt gamma rays. For comparison, the conventional measurements by detecting neutrons were also performed. These measurements were carried out in the subcriticality range from 0 to $1.8. The gate-time dependence of the variance-and covariance-to-mean ratios measured by gamma-ray detection were nearly identical with those obtained using standard neutron-detection techniques. Consequently, the prompt-neutron decay constants inferred from the gamma-ray correlation data agreed with those from the neutron data. Furthermore, the correlated-to-uncorrelated amplitude ratios obtained by gamma-ray detection significantly depended on the low-energy discriminator level of the single-channel analyzer. The discriminator level was determined as optimum for obtaining a maximum value of the amplitude ratio. The maximum amplitude ratio was much larger than that obtained by neutron detection. The subcriticality dependence of the decay constant obtained by gamma-ray detection was consistent with that obtained by neutron detection and followed the linear relation based on the one-point kinetic model in the vicinity of delayed critical. These experimental results suggest that the gamma-ray correlation technique can be applied to measure reactor kinetic parameters more efficiently

  16. Leading singularities and off-shell conformal integrals

    Energy Technology Data Exchange (ETDEWEB)

    Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.

    2013-08-29

    The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.

  17. Multi-agent sequential hypothesis testing

    KAUST Repository

    Kim, Kwang-Ki K.

    2014-12-15

    This paper considers multi-agent sequential hypothesis testing and presents a framework for strategic learning in sequential games with explicit consideration of both temporal and spatial coordination. The associated Bayes risk functions explicitly incorporate costs of taking private/public measurements, costs of time-difference and disagreement in actions of agents, and costs of false declaration/choices in the sequential hypothesis testing. The corresponding sequential decision processes have well-defined value functions with respect to (a) the belief states for the case of conditional independent private noisy measurements that are also assumed to be independent identically distributed over time, and (b) the information states for the case of correlated private noisy measurements. A sequential investment game of strategic coordination and delay is also discussed as an application of the proposed strategic learning rules.

  18. Pre-asymptotic behavior of single-particle overlap integrals of non-Borromean two-neutron halos

    International Nuclear Information System (INIS)

    Timofeyuk, N.K.; Tostevin, J.A.; Blokhintsev, L.D.

    2003-01-01

    For non-Borromean two-neutron halo nuclei, modifications to the behavior of single-particle overlap integrals will arise due to the correlations of the two interacting nucleons in the halo. An additional contribution to the overlap integral can be obtained using the Feynman diagram approach. This additional term is modeled using a simple local potential model. We show that these modifications may play a role in detailed interpretations of experimental results from single-nucleon knockout, transfer, and other reactions that probe the single-nucleon overlap functions

  19. Simultaneous integrated vs. sequential boost in VMAT radiotherapy of high-grade gliomas.

    Science.gov (United States)

    Farzin, Mostafa; Molls, Michael; Astner, Sabrina; Rondak, Ina-Christine; Oechsner, Markus

    2015-12-01

    In 20 patients with high-grade gliomas, we compared two methods of planning for volumetric-modulated arc therapy (VMAT): simultaneous integrated boost (SIB) vs. sequential boost (SEB). The investigation focused on the analysis of dose distributions in the target volumes and the organs at risk (OARs). After contouring the target volumes [planning target volumes (PTVs) and boost volumes (BVs)] and OARs, SIB planning and SEB planning were performed. The SEB method consisted of two plans: in the first plan the PTV received 50 Gy in 25 fractions with a 2-Gy dose per fraction. In the second plan the BV received 10 Gy in 5 fractions with a dose per fraction of 2 Gy. The doses of both plans were summed up to show the total doses delivered. In the SIB method the PTV received 54 Gy in 30 fractions with a dose per fraction of 1.8 Gy, while the BV received 60 Gy in the same fraction number but with a dose per fraction of 2 Gy. All of the OARs showed higher doses (Dmax and Dmean) in the SEB method when compared with the SIB technique. The differences between the two methods were statistically significant in almost all of the OARs. Analysing the total doses of the target volumes we found dose distributions with similar homogeneities and comparable total doses. Our analysis shows that the SIB method offers advantages over the SEB method in terms of sparing OARs.

  20. Accumulation of evidence during sequential decision making: the importance of top-down factors.

    Science.gov (United States)

    de Lange, Floris P; Jensen, Ole; Dehaene, Stanislas

    2010-01-13

    In the last decade, great progress has been made in characterizing the accumulation of neural information during simple unitary perceptual decisions. However, much less is known about how sequentially presented evidence is integrated over time for successful decision making. The aim of this study was to study the mechanisms of sequential decision making in humans. In a magnetoencephalography (MEG) study, we presented healthy volunteers with sequences of centrally presented arrows. Sequence length varied between one and five arrows, and the accumulated directions of the arrows informed the subject about which hand to use for a button press at the end of the sequence (e.g., LRLRR should result in a right-hand press). Mathematical modeling suggested that nonlinear accumulation was the rational strategy for performing this task in the presence of no or little noise, whereas quasilinear accumulation was optimal in the presence of substantial noise. MEG recordings showed a correlate of evidence integration over parietal and central cortex that was inversely related to the amount of accumulated evidence (i.e., when more evidence was accumulated, neural activity for new stimuli was attenuated). This modulation of activity likely reflects a top-down influence on sensory processing, effectively constraining the influence of sensory information on the decision variable over time. The results indicate that, when making decisions on the basis of sequential information, the human nervous system integrates evidence in a nonlinear manner, using the amount of previously accumulated information to constrain the accumulation of additional evidence.

  1. Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator

    International Nuclear Information System (INIS)

    Decanini, Yves; Folacci, Antoine

    2006-01-01

    Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients--i.e., the DeWitt and Hadamard coefficients--that define them

  2. JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes

    Science.gov (United States)

    Binosi, D.; Collins, J.; Kaufhold, C.; Theussl, L.

    2009-09-01

    A new version of the Feynman graph plotting tool JaxoDraw is presented. Version 2.0 is a fundamental re-write of most of the JaxoDraw core and some functionalities, in particular importing graphs, are not backward-compatible with the 1.x branch. The most prominent new features include: drawing of Bézier curves for all particle modes, on-the-fly update of edited objects, multiple undo/redo functionality, the addition of a plugin infrastructure, and a general improved memory performance. A new LaTeX style file is presented that has been written specifically on top of the original axodraw.sty to meet the needs of this new version. New version program summaryProgram title: JaxoDraw Catalogue identifier: ADUA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 103 544 No. of bytes in distributed program, including test data, etc.: 3 745 814 Distribution format: tar.gz Programming language: Java Computer: Any Java-enabled platform Operating system: Any Java-enabled platform, tested on Linux, Windows XP, Mac OS X Classification: 14 Catalogue identifier of previous version: ADUA_v1_0 Journal reference of previous version: Comput. Phys. Comm. 161 (2004) 76 Does the new version supersede the previous version?: Yes Nature of problem: Existing methods for drawing Feynman diagrams usually require some hard-coding in one or the other programming or scripting language. It is not very convenient and often time consuming, to generate relatively simple diagrams. Solution method: A program is provided that allows for the interactive drawing of Feynman diagrams with a graphical user interface. The program is easy to learn and use, produces high quality output in several formats and runs on any operating system where a Java Runtime Environment is available. Reasons for new version: A

  3. Sequential charged particle reaction

    International Nuclear Information System (INIS)

    Hori, Jun-ichi; Ochiai, Kentaro; Sato, Satoshi; Yamauchi, Michinori; Nishitani, Takeo

    2004-01-01

    The effective cross sections for producing the sequential reaction products in F82H, pure vanadium and LiF with respect to the 14.9-MeV neutron were obtained and compared with the estimation ones. Since the sequential reactions depend on the secondary charged particles behavior, the effective cross sections are corresponding to the target nuclei and the material composition. The effective cross sections were also estimated by using the EAF-libraries and compared with the experimental ones. There were large discrepancies between estimated and experimental values. Additionally, we showed the contribution of the sequential reaction on the induced activity and dose rate in the boundary region with water. From the present study, it has been clarified that the sequential reactions are of great importance to evaluate the dose rates around the surface of cooling pipe and the activated corrosion products. (author)

  4. Effective multiplication factor measurement by feynman-α method. 3

    International Nuclear Information System (INIS)

    Mouri, Tomoaki; Ohtani, Nobuo

    1998-06-01

    The sub-criticality monitoring system has been developed for criticality safety control in nuclear fuel handling plants. In the past experiments performed with the Deuterium Critical Assembly (DCA), it was confirmed that the detection of sub-criticality was possible to k eff = 0.3. To investigate the applicability of the method to more generalized system, experiments were performed in the light-water-moderated system of the modified DCA core. From these experiments, it was confirmed that the prompt decay constant (α), which was a index of the sub-criticality, was detected between k eff = 0.623 and k eff = 0.870 and the difference of 0.05 - 0.1Δk could be distinguished. The α values were numerically calculated with 2D transport code TWODANT and monte carlo code KENO V.a, and the results were compared with the measured values. The differences between calculated and measured values were proved to be less than 13%, which was sufficient accuracy in the sub-criticality monitoring system. It was confirmed that Feynman-α method was applicable to sub-critical measurement of the light-water-moderated system. (author)

  5. Feynman path integral application on deriving black-scholes diffusion equation for european option pricing

    International Nuclear Information System (INIS)

    Utama, Briandhika; Purqon, Acep

    2016-01-01

    Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods. (paper)

  6. Organization principles in visual working memory: Evidence from sequential stimulus display.

    Science.gov (United States)

    Gao, Zaifeng; Gao, Qiyang; Tang, Ning; Shui, Rende; Shen, Mowei

    2016-01-01

    Although the mechanisms of visual working memory (VWM) have been studied extensively in recent years, the active property of VWM has received less attention. In the current study, we examined how VWM integrates sequentially presented stimuli by focusing on the role of Gestalt principles, which are important organizing principles in perceptual integration. We manipulated the level of Gestalt cues among three or four sequentially presented objects that were memorized. The Gestalt principle could not emerge unless all the objects appeared together. We distinguished two hypotheses: a perception-alike hypothesis and an encoding-specificity hypothesis. The former predicts that the Gestalt cue will play a role in information integration within VWM; the latter predicts that the Gestalt cue will not operate within VWM. In four experiments, we demonstrated that collinearity (Experiment 1) and closure (Experiment 2) cues significantly improved VWM performance, and this facilitation was not affected by the testing manner (Experiment 3) or by adding extra colors to the memorized objects (Experiment 4). Finally, we re-established the Gestalt cue benefit with similarity cues (Experiment 5). These findings together suggest that VWM realizes and uses potential Gestalt principles within the stored representations, supporting a perception-alike hypothesis. Copyright © 2015 Elsevier B.V. All rights reserved.

  7. Moving mesh generation with a sequential approach for solving PDEs

    DEFF Research Database (Denmark)

    In moving mesh methods, physical PDEs and a mesh equation derived from equidistribution of an error metrics (so-called the monitor function) are simultaneously solved and meshes are dynamically concentrated on steep regions (Lim et al., 2001). However, the simultaneous solution procedure...... a simple and robust moving mesh algorithm in one or multidimension. In this study, we propose a sequential solution procedure including two separate parts: prediction step to obtain an approximate solution to a next time level (integration of physical PDEs) and regriding step at the next time level (mesh...... generation and solution interpolation). Convection terms, which appear in physical PDEs and a mesh equation, are discretized by a WENO (Weighted Essentially Non-Oscillatory) scheme under the consrvative form. This sequential approach is to keep the advantages of robustness and simplicity for the static...

  8. Reduction method for one-loop tensor 5- and 6-point integrals revisited

    International Nuclear Information System (INIS)

    Diakonidis, Theodoros

    2009-01-01

    A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)

  9. Reduction method for one-loop tensor 5- and 6-point integrals revisited

    Energy Technology Data Exchange (ETDEWEB)

    Diakonidis, Theodoros [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2009-01-15

    A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)

  10. Comments on the sequential probability ratio testing methods

    Energy Technology Data Exchange (ETDEWEB)

    Racz, A. [Hungarian Academy of Sciences, Budapest (Hungary). Central Research Inst. for Physics

    1996-07-01

    In this paper the classical sequential probability ratio testing method (SPRT) is reconsidered. Every individual boundary crossing event of the SPRT is regarded as a new piece of evidence about the problem under hypothesis testing. The Bayes method is applied for belief updating, i.e. integrating these individual decisions. The procedure is recommended to use when the user (1) would like to be informed about the tested hypothesis continuously and (2) would like to achieve his final conclusion with high confidence level. (Author).

  11. Quantum density fluctuations in liquid neon from linearized path-integral calculations

    International Nuclear Information System (INIS)

    Poulsen, Jens Aage; Scheers, Johan; Nyman, Gunnar; Rossky, Peter J.

    2007-01-01

    The Feynman-Kleinert linearized path-integral [J. A. Poulsen et al., J. Chem. Phys. 119, 12179 (2003)] representation of quantum correlation functions is applied to compute the spectrum of density fluctuations for liquid neon at T=27.6 K, p=1.4 bar, and Q vector 1.55 Aa -1 . The calculated spectrum as well as the kinetic energy of the liquid are in excellent agreement with the experiment of Cunsolo et al. [Phys. Rev. B 67, 024507 (2003)

  12. New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

    Science.gov (United States)

    Volkov, Sergey

    2017-11-01

    This paper presents a new method of numerical computation of the mass-independent QED contributions to the electron anomalous magnetic moment which arise from Feynman graphs without closed electron loops. The method is based on a forestlike subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph before integration in Feynman-parametric space. The integration is performed by an importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs, and to some individual 5-loop graphs are presented, as well as the comparison of this method with other ones with respect to Monte Carlo convergence speed.

  13. Remarks on sequential designs in risk assessment

    International Nuclear Information System (INIS)

    Seidenfeld, T.

    1982-01-01

    The special merits of sequential designs are reviewed in light of particular challenges that attend risk assessment for human population. The kinds of ''statistical inference'' are distinguished and the problem of design which is pursued is the clash between Neyman-Pearson and Bayesian programs of sequential design. The value of sequential designs is discussed and the Neyman-Pearson vs. Bayesian sequential designs are probed in particular. Finally, warnings with sequential designs are considered, especially in relation to utilitarianism

  14. Dosimetric comparison of standard three-dimensional conformal radiotherapy followed by intensity-modulated radiotherapy boost schedule (sequential IMRT plan) with simultaneous integrated boost-IMRT (SIB IMRT) treatment plan in patients with localized carcinoma prostate.

    Science.gov (United States)

    Bansal, A; Kapoor, R; Singh, S K; Kumar, N; Oinam, A S; Sharma, S C

    2012-07-01

    DOSIMETERIC AND RADIOBIOLOGICAL COMPARISON OF TWO RADIATION SCHEDULES IN LOCALIZED CARCINOMA PROSTATE: Standard Three-Dimensional Conformal Radiotherapy (3DCRT) followed by Intensity Modulated Radiotherapy (IMRT) boost (sequential-IMRT) with Simultaneous Integrated Boost IMRT (SIB-IMRT). Thirty patients were enrolled. In all, the target consisted of PTV P + SV (Prostate and seminal vesicles) and PTV LN (lymph nodes) where PTV refers to planning target volume and the critical structures included: bladder, rectum and small bowel. All patients were treated with sequential-IMRT plan, but for dosimetric comparison, SIB-IMRT plan was also created. The prescription dose to PTV P + SV was 74 Gy in both strategies but with different dose per fraction, however, the dose to PTV LN was 50 Gy delivered in 25 fractions over 5 weeks for sequential-IMRT and 54 Gy delivered in 27 fractions over 5.5 weeks for SIB-IMRT. The treatment plans were compared in terms of dose-volume histograms. Also, Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) obtained with the two plans were compared. The volume of rectum receiving 70 Gy or more (V > 70 Gy) was reduced to 18.23% with SIB-IMRT from 22.81% with sequential-IMRT. SIB-IMRT reduced the mean doses to both bladder and rectum by 13% and 17%, respectively, as compared to sequential-IMRT. NTCP of 0.86 ± 0.75% and 0.01 ± 0.02% for the bladder, 5.87 ± 2.58% and 4.31 ± 2.61% for the rectum and 8.83 ± 7.08% and 8.25 ± 7.98% for the bowel was seen with sequential-IMRT and SIB-IMRT plans respectively. For equal PTV coverage, SIB-IMRT markedly reduced doses to critical structures, therefore should be considered as the strategy for dose escalation. SIB-IMRT achieves lesser NTCP than sequential-IMRT.

  15. A solution for tensor reduction of one-loop N-point functions with N{>=}6

    Energy Technology Data Exchange (ETDEWEB)

    Fleischer, J. [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2011-11-15

    Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N{>=}6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N-1)-point Feynman integrals of rank (R-1) (for N{>=}6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization. (orig.)

  16. Coupled inflaton and electromagnetic fields from Gravitoelectromagnetic Inflation with Lorentz and Feynman gauges

    International Nuclear Information System (INIS)

    Membiela, Federico Agustín; Bellini, Mauricio

    2010-01-01

    Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. We use simultaneously the Lorentz and Feynman gauges. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of electric and magnetic field modes during the early inflationary epoch of the universe on cosmological scales. This is the first time that solutions for the electric field fluctuations are investigated in a systematic way as embeddings for inflationary models in 4D. An important and new result here obtained is that the spectrum of the electric field fluctuations depend with the scale, such that the spectral index increases quadratically as the scale decreases

  17. Coupled inflaton and electromagnetic fields from Gravitoelectromagnetic Inflation with Lorentz and Feynman gauges

    Energy Technology Data Exchange (ETDEWEB)

    Membiela, Federico Agustín; Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar, E-mail: membiela@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, (7600) Mar del Plata (Argentina)

    2010-10-01

    Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. We use simultaneously the Lorentz and Feynman gauges. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of electric and magnetic field modes during the early inflationary epoch of the universe on cosmological scales. This is the first time that solutions for the electric field fluctuations are investigated in a systematic way as embeddings for inflationary models in 4D. An important and new result here obtained is that the spectrum of the electric field fluctuations depend with the scale, such that the spectral index increases quadratically as the scale decreases.

  18. Sequential lineup laps and eyewitness accuracy.

    Science.gov (United States)

    Steblay, Nancy K; Dietrich, Hannah L; Ryan, Shannon L; Raczynski, Jeanette L; James, Kali A

    2011-08-01

    Police practice of double-blind sequential lineups prompts a question about the efficacy of repeated viewings (laps) of the sequential lineup. Two laboratory experiments confirmed the presence of a sequential lap effect: an increase in witness lineup picks from first to second lap, when the culprit was a stranger. The second lap produced more errors than correct identifications. In Experiment 2, lineup diagnosticity was significantly higher for sequential lineup procedures that employed a single versus double laps. Witnesses who elected to view a second lap made significantly more errors than witnesses who chose to stop after one lap or those who were required to view two laps. Witnesses with prior exposure to the culprit did not exhibit a sequential lap effect.

  19. New dual conformally invariant off-shell integrals

    International Nuclear Information System (INIS)

    Nguyen, Dung; Spradlin, Marcus; Volovich, Anastasia

    2008-01-01

    Evidence has recently emerged for a hidden symmetry of planar scattering amplitudes in N=4 super-Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS 5 . In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities

  20. Robustness of the Sequential Lineup Advantage

    Science.gov (United States)

    Gronlund, Scott D.; Carlson, Curt A.; Dailey, Sarah B.; Goodsell, Charles A.

    2009-01-01

    A growing movement in the United States and around the world involves promoting the advantages of conducting an eyewitness lineup in a sequential manner. We conducted a large study (N = 2,529) that included 24 comparisons of sequential versus simultaneous lineups. A liberal statistical criterion revealed only 2 significant sequential lineup…

  1. Sequential capillary electrophoresis analysis using optically gated sample injection and UV/vis detection.

    Science.gov (United States)

    Liu, Xiaoxia; Tian, Miaomiao; Camara, Mohamed Amara; Guo, Liping; Yang, Li

    2015-10-01

    We present sequential CE analysis of amino acids and L-asparaginase-catalyzed enzyme reaction, by combing the on-line derivatization, optically gated (OG) injection and commercial-available UV-Vis detection. Various experimental conditions for sequential OG-UV/vis CE analysis were investigated and optimized by analyzing a standard mixture of amino acids. High reproducibility of the sequential CE analysis was demonstrated with RSD values (n = 20) of 2.23, 2.57, and 0.70% for peak heights, peak areas, and migration times, respectively, and the LOD of 5.0 μM (for asparagine) and 2.0 μM (for aspartic acid) were obtained. With the application of the OG-UV/vis CE analysis, sequential online CE enzyme assay of L-asparaginase-catalyzed enzyme reaction was carried out by automatically and continuously monitoring the substrate consumption and the product formation every 12 s from the beginning to the end of the reaction. The Michaelis constants for the reaction were obtained and were found to be in good agreement with the results of traditional off-line enzyme assays. The study demonstrated the feasibility and reliability of integrating the OG injection with UV/vis detection for sequential online CE analysis, which could be of potential value for online monitoring various chemical reaction and bioprocesses. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  2. Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

    Science.gov (United States)

    Putz, Mihai V

    2009-11-10

    The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

  3. Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

    Directory of Open Access Journals (Sweden)

    Mihai V. Putz

    2009-11-01

    Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.

  4. WKB wave function for many-variable systems

    International Nuclear Information System (INIS)

    Sakita, B.; Tzani, R.

    1986-01-01

    The WKB method is a non-perturbative semi-classical method in quantum mechanics. The method for a system of one degree of freedom is well known and described in standard textbooks. The method for a system with many degrees of freedom especially for quantum fields is more involved. There exist two methods: Feynman path integral and Schrodinger wave function. The Feynman path integral WKB method is essentially a stationary phase approximation for Feynman path integrals. The WKB Schrodinger wave function method is on the other hand an extension of the standard WKB to many-variable systems

  5. Microcanonical functional integral for the gravitational field

    International Nuclear Information System (INIS)

    Brown, J.D.; York, J.W. Jr.

    1993-01-01

    The gravitational field in a spatially finite region is described as a microcanonical system. The density of states ν is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by any real stationary axisymmetric black hole, then in this same approximation lnν is shown to equal 1/4 the area of the black-hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of ν that lead to ''imaginary-time'' functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function

  6. Multi-agent sequential hypothesis testing

    KAUST Repository

    Kim, Kwang-Ki K.; Shamma, Jeff S.

    2014-01-01

    incorporate costs of taking private/public measurements, costs of time-difference and disagreement in actions of agents, and costs of false declaration/choices in the sequential hypothesis testing. The corresponding sequential decision processes have well

  7. Feynman amplitude and the Meijer's function. A unified representation for divergent and convergent graphs

    Energy Technology Data Exchange (ETDEWEB)

    Kucheryavyi, V I

    1974-12-31

    A parametric alpha -representation of Feynman amplitude for any spinor graph, which is expressed in terms of the Meijer's G functions, is obtained. This representation is valid both for divergent and convergent graphs. The available ChisholmNakanishi-Symanzik alpha -representation for convergent scalar graph turns out to be a special of the formula obtained. Besides that, the expression has a number of useful features. This representation automatically removes the infrared divergencies connected with zero photon mass. The expression has a form in which the scale-invariant terms are explicitly separated from the terms breaking the invariance. It is shown by considering the simplest graphs of quantum electrodynamics that this representation keeps gauge invariance and Ward's identity for renormalized amplitudes. (auth)

  8. Sequential stochastic optimization

    CERN Document Server

    Cairoli, Renzo

    1996-01-01

    Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet

  9. Sequential Ground Motion Effects on the Behavior of a Base-Isolated RCC Building

    Directory of Open Access Journals (Sweden)

    Zhi Zheng

    2017-01-01

    Full Text Available The sequential ground motion effects on the dynamic responses of reinforced concrete containment (RCC buildings with typical isolators are studied in this paper. Although the base isolation technique is developed to guarantee the security and integrity of RCC buildings under single earthquakes, seismic behavior of base-isolated RCC buildings under sequential ground motions is deficient. Hence, an ensemble of as-recorded sequential ground motions is employed to study the effect of including aftershocks on the seismic evaluation of base-isolated RCC buildings. The results indicate that base isolation can significantly attenuate the earthquake shaking of the RCC building under not only single earthquakes but also seismic sequences. It is also found that the adverse aftershock effect on the RCC can be reduced due to the base isolation applied to the RCC. More importantly, the study indicates that disregarding aftershocks can induce significant underestimation of the isolator displacement for base-isolated RCC buildings.

  10. Heuristic and optimal policy computations in the human brain during sequential decision-making.

    Science.gov (United States)

    Korn, Christoph W; Bach, Dominik R

    2018-01-23

    Optimal decisions across extended time horizons require value calculations over multiple probabilistic future states. Humans may circumvent such complex computations by resorting to easy-to-compute heuristics that approximate optimal solutions. To probe the potential interplay between heuristic and optimal computations, we develop a novel sequential decision-making task, framed as virtual foraging in which participants have to avoid virtual starvation. Rewards depend only on final outcomes over five-trial blocks, necessitating planning over five sequential decisions and probabilistic outcomes. Here, we report model comparisons demonstrating that participants primarily rely on the best available heuristic but also use the normatively optimal policy. FMRI signals in medial prefrontal cortex (MPFC) relate to heuristic and optimal policies and associated choice uncertainties. Crucially, reaction times and dorsal MPFC activity scale with discrepancies between heuristic and optimal policies. Thus, sequential decision-making in humans may emerge from integration between heuristic and optimal policies, implemented by controllers in MPFC.

  11. Exploring the sequential lineup advantage using WITNESS.

    Science.gov (United States)

    Goodsell, Charles A; Gronlund, Scott D; Carlson, Curt A

    2010-12-01

    Advocates claim that the sequential lineup is an improvement over simultaneous lineup procedures, but no formal (quantitatively specified) explanation exists for why it is better. The computational model WITNESS (Clark, Appl Cogn Psychol 17:629-654, 2003) was used to develop theoretical explanations for the sequential lineup advantage. In its current form, WITNESS produced a sequential advantage only by pairing conservative sequential choosing with liberal simultaneous choosing. However, this combination failed to approximate four extant experiments that exhibited large sequential advantages. Two of these experiments became the focus of our efforts because the data were uncontaminated by likely suspect position effects. Decision-based and memory-based modifications to WITNESS approximated the data and produced a sequential advantage. The next step is to evaluate the proposed explanations and modify public policy recommendations accordingly.

  12. Sequential memory: Binding dynamics

    Science.gov (United States)

    Afraimovich, Valentin; Gong, Xue; Rabinovich, Mikhail

    2015-10-01

    Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories—episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L - 1, where L is the number of modalities.

  13. Cross section evaluation by spinor integration: The massless case in 4D

    International Nuclear Information System (INIS)

    Feng Bo; Huang Rijun; Jia Yin; Luo Mingxing; Wang Honghui

    2010-01-01

    To get the total cross section of one interaction from its amplitude M, one needs to integrate |M| 2 over phase spaces of all outgoing particles. Starting from this paper, we will propose a new method to perform such integrations, which is inspired by the reduced phase space integration of one-loop unitarity cut developed in the last few years. The new method reduces one constrained three-dimension momentum space integration to a one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. The current paper is the first paper of a series for the new method. Here we have exclusively focused on massless particles in 4D. There is no need to carve out a complicated integration region in the phase space for this particular simple case because the integration region is always simply [0,1].

  14. Ray optics for diffraction: a useful paradox in a path integral context

    International Nuclear Information System (INIS)

    Schulman, L.S.

    1984-01-01

    Geometrical diffraction theory uses ray tracing techniques to calculate diffraction and other properties of the electromagnetic field generally considered characteristically wave like. The author studies this dualism of the classical electromagnetic field so as to distinguish those aspects of quantum dualism that arise simply as properties of oscillatory integrals and those that may have deeper origins. By a series of transformations the solutions of certain optics problems are reduced to the evaluation of a Feynman path integral and the known semiclassical approximations for the path integral provide a justification for the geometrical diffraction theory. Particular attention is paid to the problem of edge diffraction and for a half plane barrier a closed form solution is obtained. A classical variational principle for barrier penetration is also presented. (Auth.)

  15. A novel system for simultaneous or sequential integration of multiple gene-loading vectors into a defined site of a human artificial chromosome.

    Science.gov (United States)

    Suzuki, Teruhiko; Kazuki, Yasuhiro; Oshimura, Mitsuo; Hara, Takahiko

    2014-01-01

    Human artificial chromosomes (HACs) are gene-delivery vectors suitable for introducing large DNA fragments into mammalian cells. Although a HAC theoretically incorporates multiple gene expression cassettes of unlimited DNA size, its application has been limited because the conventional gene-loading system accepts only one gene-loading vector (GLV) into a HAC. We report a novel method for the simultaneous or sequential integration of multiple GLVs into a HAC vector (designated as the SIM system) via combined usage of Cre, FLP, Bxb1, and φC31 recombinase/integrase. As a proof of principle, we first attempted simultaneous integration of three GLVs encoding EGFP, Venus, and TdTomato into a gene-loading site of a HAC in CHO cells. These cells successfully expressed all three fluorescent proteins. Furthermore, microcell-mediated transfer of HACs enabled the expression of those fluorescent proteins in recipient cells. We next demonstrated that GLVs could be introduced into a HAC one-by-one via reciprocal usage of recombinase/integrase. Lastly, we introduced a fourth GLV into a HAC after simultaneous integration of three GLVs by FLP-mediated DNA recombination. The SIM system expands the applicability of HAC vectors and is useful for various biomedical studies, including cell reprogramming.

  16. A novel system for simultaneous or sequential integration of multiple gene-loading vectors into a defined site of a human artificial chromosome.

    Directory of Open Access Journals (Sweden)

    Teruhiko Suzuki

    Full Text Available Human artificial chromosomes (HACs are gene-delivery vectors suitable for introducing large DNA fragments into mammalian cells. Although a HAC theoretically incorporates multiple gene expression cassettes of unlimited DNA size, its application has been limited because the conventional gene-loading system accepts only one gene-loading vector (GLV into a HAC. We report a novel method for the simultaneous or sequential integration of multiple GLVs into a HAC vector (designated as the SIM system via combined usage of Cre, FLP, Bxb1, and φC31 recombinase/integrase. As a proof of principle, we first attempted simultaneous integration of three GLVs encoding EGFP, Venus, and TdTomato into a gene-loading site of a HAC in CHO cells. These cells successfully expressed all three fluorescent proteins. Furthermore, microcell-mediated transfer of HACs enabled the expression of those fluorescent proteins in recipient cells. We next demonstrated that GLVs could be introduced into a HAC one-by-one via reciprocal usage of recombinase/integrase. Lastly, we introduced a fourth GLV into a HAC after simultaneous integration of three GLVs by FLP-mediated DNA recombination. The SIM system expands the applicability of HAC vectors and is useful for various biomedical studies, including cell reprogramming.

  17. Achieving Integration in Mixed Methods Designs—Principles and Practices

    OpenAIRE

    Fetters, Michael D; Curry, Leslie A; Creswell, John W

    2013-01-01

    Mixed methods research offers powerful tools for investigating complex processes and systems in health and health care. This article describes integration principles and practices at three levels in mixed methods research and provides illustrative examples. Integration at the study design level occurs through three basic mixed method designs—exploratory sequential, explanatory sequential, and convergent—and through four advanced frameworks—multistage, intervention, case study, and participato...

  18. Sequential Probability Ration Tests : Conservative and Robust

    NARCIS (Netherlands)

    Kleijnen, J.P.C.; Shi, Wen

    2017-01-01

    In practice, most computers generate simulation outputs sequentially, so it is attractive to analyze these outputs through sequential statistical methods such as sequential probability ratio tests (SPRTs). We investigate several SPRTs for choosing between two hypothesized values for the mean output

  19. Optical propagators in vector and spinor theories by path integral formalism

    International Nuclear Information System (INIS)

    Linares, J.

    1993-01-01

    The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs

  20. Sequential lineup presentation: Patterns and policy

    OpenAIRE

    Lindsay, R C L; Mansour, Jamal K; Beaudry, J L; Leach, A-M; Bertrand, M I

    2009-01-01

    Sequential lineups were offered as an alternative to the traditional simultaneous lineup. Sequential lineups reduce incorrect lineup selections; however, the accompanying loss of correct identifications has resulted in controversy regarding adoption of the technique. We discuss the procedure and research relevant to (1) the pattern of results found using sequential versus simultaneous lineups; (2) reasons (theory) for differences in witness responses; (3) two methodological issues; and (4) im...

  1. Sequential Product of Quantum Effects: An Overview

    Science.gov (United States)

    Gudder, Stan

    2010-12-01

    This article presents an overview for the theory of sequential products of quantum effects. We first summarize some of the highlights of this relatively recent field of investigation and then provide some new results. We begin by discussing sequential effect algebras which are effect algebras endowed with a sequential product satisfying certain basic conditions. We then consider sequential products of (discrete) quantum measurements. We next treat transition effect matrices (TEMs) and their associated sequential product. A TEM is a matrix whose entries are effects and whose rows form quantum measurements. We show that TEMs can be employed for the study of quantum Markov chains. Finally, we prove some new results concerning TEMs and vector densities.

  2. Optimal Sequential Rules for Computer-Based Instruction.

    Science.gov (United States)

    Vos, Hans J.

    1998-01-01

    Formulates sequential rules for adapting the appropriate amount of instruction to learning needs in the context of computer-based instruction. Topics include Bayesian decision theory, threshold and linear-utility structure, psychometric model, optimal sequential number of test questions, and an empirical example of sequential instructional…

  3. Sequential vs simultaneous encoding of spatial information: a comparison between the blind and the sighted.

    Science.gov (United States)

    Ruotolo, Francesco; Ruggiero, Gennaro; Vinciguerra, Michela; Iachini, Tina

    2012-02-01

    The aim of this research is to assess whether the crucial factor in determining the characteristics of blind people's spatial mental images is concerned with the visual impairment per se or the processing style that the dominant perceptual modalities used to acquire spatial information impose, i.e. simultaneous (vision) vs sequential (kinaesthesis). Participants were asked to learn six positions in a large parking area via movement alone (congenitally blind, adventitiously blind, blindfolded sighted) or with vision plus movement (simultaneous sighted, sequential sighted), and then to mentally scan between positions in the path. The crucial manipulation concerned the sequential sighted group. Their visual exploration was made sequential by putting visual obstacles within the pathway in such a way that they could not see simultaneously the positions along the pathway. The results revealed a significant time/distance linear relation in all tested groups. However, the linear component was lower in sequential sighted and blind participants, especially congenital. Sequential sighted and congenitally blind participants showed an almost overlapping performance. Differences between groups became evident when mentally scanning farther distances (more than 5m). This threshold effect could be revealing of processing limitations due to the need of integrating and updating spatial information. Overall, the results suggest that the characteristics of the processing style rather than the visual impairment per se affect blind people's spatial mental images. Copyright © 2011 Elsevier B.V. All rights reserved.

  4. Continual integration method in the polaron model

    International Nuclear Information System (INIS)

    Kochetov, E.A.; Kuleshov, S.P.; Smondyrev, M.A.

    1981-01-01

    The article is devoted to the investigation of a polaron system on the base of a variational approach formulated on the language of continuum integration. The variational method generalizing the Feynman one for the case of the system pulse different from zero has been formulated. The polaron state has been investigated at zero temperature. A problem of the bound state of two polarons exchanging quanta of a scalar field as well as a problem of polaron scattering with an external field in the Born approximation have been considered. Thermodynamics of the polaron system has been investigated, namely, high-temperature expansions for mean energy and effective polaron mass have been studied [ru

  5. Nuclear physics aspects in the parton model of Feynman

    International Nuclear Information System (INIS)

    Pauchy Hwang, W.Y.

    1995-01-01

    The basic fact that pions couple strongly to nucleons has dominated various nuclear physics thinkings since the birth of the field more than sixty years ago. The parton model of Feynman, in which the structure of a nucleon (or a hadron) is characterized by a set of parton distributions, was proposed originally in late 1960's to treat high energy deep inelastic scattering, and later many other high energy physics experiments involving hadrons. Introduction of the concept of parton distributions signifies the departure of particle physics from nuclear physics. Following the suggestion that the sea quark distributions in a nucleon, at low and moderate Q 2 (at least up to a few GeV 2 ), can be attributed primarily to the probability of finding such quarks or antiquarks in the mesons (or recoiling baryons) associated with the nucleon, the author examines how nuclear physics aspects offer quantitative understanding of several recent experimental results, including the observed violation of the Gotfried sum rule and the so-called open-quotes proton spin crisisclose quotes. These results suggest that determination of parton distributions of a hadron at Q 2 of a few GeV 2 (and at small x) must in general take into account nuclear physics aspects. Implication of these results for other high-energy reactions, such as semi-inclusive hadron production in deep inelastic scattering, are also discussed

  6. Implementing reduced-risk integrated pest management in fresh-market cabbage: influence of sampling parameters, and validation of binomial sequential sampling plans for the cabbage looper (Lepidoptera Noctuidae).

    Science.gov (United States)

    Burkness, Eric C; Hutchison, W D

    2009-10-01

    Populations of cabbage looper, Trichoplusiani (Lepidoptera: Noctuidae), were sampled in experimental plots and commercial fields of cabbage (Brasicca spp.) in Minnesota during 1998-1999 as part of a larger effort to implement an integrated pest management program. Using a resampling approach and the Wald's sequential probability ratio test, sampling plans with different sampling parameters were evaluated using independent presence/absence and enumerative data. Evaluations and comparisons of the different sampling plans were made based on the operating characteristic and average sample number functions generated for each plan and through the use of a decision probability matrix. Values for upper and lower decision boundaries, sequential error rates (alpha, beta), and tally threshold were modified to determine parameter influence on the operating characteristic and average sample number functions. The following parameters resulted in the most desirable operating characteristic and average sample number functions; action threshold of 0.1 proportion of plants infested, tally threshold of 1, alpha = beta = 0.1, upper boundary of 0.15, lower boundary of 0.05, and resampling with replacement. We found that sampling parameters can be modified and evaluated using resampling software to achieve desirable operating characteristic and average sample number functions. Moreover, management of T. ni by using binomial sequential sampling should provide a good balance between cost and reliability by minimizing sample size and maintaining a high level of correct decisions (>95%) to treat or not treat.

  7. Simultaneous optimization of sequential IMRT plans

    International Nuclear Information System (INIS)

    Popple, Richard A.; Prellop, Perri B.; Spencer, Sharon A.; Santos, Jennifer F. de los; Duan, Jun; Fiveash, John B.; Brezovich, Ivan A.

    2005-01-01

    Radiotherapy often comprises two phases, in which irradiation of a volume at risk for microscopic disease is followed by a sequential dose escalation to a smaller volume either at a higher risk for microscopic disease or containing only gross disease. This technique is difficult to implement with intensity modulated radiotherapy, as the tolerance doses of critical structures must be respected over the sum of the two plans. Techniques that include an integrated boost have been proposed to address this problem. However, clinical experience with such techniques is limited, and many clinicians are uncomfortable prescribing nonconventional fractionation schemes. To solve this problem, we developed an optimization technique that simultaneously generates sequential initial and boost IMRT plans. We have developed an optimization tool that uses a commercial treatment planning system (TPS) and a high level programming language for technical computing. The tool uses the TPS to calculate the dose deposition coefficients (DDCs) for optimization. The DDCs were imported into external software and the treatment ports duplicated to create the boost plan. The initial, boost, and tolerance doses were specified and used to construct cost functions. The initial and boost plans were optimized simultaneously using a gradient search technique. Following optimization, the fluence maps were exported to the TPS for dose calculation. Seven patients treated using sequential techniques were selected from our clinical database. The initial and boost plans used to treat these patients were developed independently of each other by dividing the tolerance doses proportionally between the initial and boost plans and then iteratively optimizing the plans until a summation that met the treatment goals was obtained. We used the simultaneous optimization technique to generate plans that met the original planning goals. The coverage of the initial and boost target volumes in the simultaneously optimized

  8. Real time alpha value measurement with Feynman-α method utilizing time series data acquisition on low enriched uranium system

    International Nuclear Information System (INIS)

    Tonoike, Kotaro; Yamamoto, Toshihiro; Watanabe, Shoichi; Miyoshi, Yoshinori

    2003-01-01

    As a part of the development of a subcriticality monitoring system, a system which has a time series data acquisition function of detector signals and a real time evaluation function of alpha value with the Feynman-alpha method was established, with which the kinetic parameter (alpha value) was measured at the STACY heterogeneous core. The Hashimoto's difference filter was implemented in the system, which enables the measurement at a critical condition. The measurement result of the new system agreed with the pulsed neutron method. (author)

  9. Quantum Inequalities and Sequential Measurements

    International Nuclear Information System (INIS)

    Candelpergher, B.; Grandouz, T.; Rubinx, J.L.

    2011-01-01

    In this article, the peculiar context of sequential measurements is chosen in order to analyze the quantum specificity in the two most famous examples of Heisenberg and Bell inequalities: Results are found at some interesting variance with customary textbook materials, where the context of initial state re-initialization is described. A key-point of the analysis is the possibility of defining Joint Probability Distributions for sequential random variables associated to quantum operators. Within the sequential context, it is shown that Joint Probability Distributions can be defined in situations where not all of the quantum operators (corresponding to random variables) do commute two by two. (authors)

  10. Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogolubov

    2015-04-01

    Full Text Available We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized.

  11. A randomized phase III study between sequential versus simultaneous integrated boost intensity-modulated radiation therapy in nasopharyngeal carcinoma.

    Science.gov (United States)

    Lertbutsayanukul, Chawalit; Prayongrat, Anussara; Kannarunimit, Danita; Chakkabat, Chakkapong; Netsawang, Buntipa; Kitpanit, Sarin

    2018-05-01

    This study was performed to compare the acute and late toxicities between sequential (SEQ) and simultaneous integrated boost (SIB) intensity-modulated radiotherapy (IMRT) in nasopharyngeal carcinoma (NPC). Stage I-IVB NPC patients were randomized to receive SEQ-IMRT or SIB-IMRT. SEQ-IMRT consisted of two plans: 2 Gy × 25 fractions to low-risk planning target volume (PTV) followed by a sequential boost (2 Gy × 10 fractions) to high-risk PTV, while SIB-IMRT treated low- and high-risk PTVs with doses of 56 and 70 Gy in 33 fractions. Toxicities and survival outcomes were analyzed. Between October 2010 and September 2015, of the 209 patients who completed treatment, 102 in the SEQ and 107 in the SIB arm were analyzed. The majority had undifferentiated squamous cell carcinoma (82%). Mucositis and dysphagia were the most common grade 3-5 acute toxicities. There were no statistically significant differences in the cumulative incidence of grade 3-4 acute toxicities between the two arms (59.8% in SEQ vs. 58.9% in SIB; P = 0.892). Common grade 3-4 late toxicities for SEQ and SIB included hearing loss (2.9 vs. 8.4%), temporal lobe injury (2.9 vs. 0.9%), cranial nerve injury (0 vs. 2.8%), and xerostomia (2 vs. 0.9%). With the median follow-up of 41 months, 3‑year progression-free and overall survival rates were 72.7 vs. 73.4% (P = 0.488) and 86.3 vs. 83.6% (P = 0.938), respectively. SEQ and SIB provide excellent survival outcomes with few late toxicities. According to our study, SIB with a satisfactory dose-volume constraint to nearby critical organs is the technique of choice for NPC treatment due to its convenience.

  12. Integral equations of hadronic correlation functions a functional- bootstrap approach

    CERN Document Server

    Manesis, E K

    1974-01-01

    A reasonable 'microscopic' foundation of the Feynman hadron-liquid analogy is offered, based on a class of models for hadron production. In an external field formalism, the equivalence (complementarity) of the exclusive and inclusive descriptions of hadronic reactions is specifically expressed in a functional-bootstrap form, and integral equations between inclusive and exclusive correlation functions are derived. Using the latest CERN-ISR data on the two-pion inclusive correlation function, and assuming rapidity translational invariance for the exclusive one, the simplest integral equation is solved in the 'central region' and an exclusive correlation length in rapidity predicted. An explanation is also offered for the unexpected similarity observed between pi /sup +/ pi /sup -/ and pi /sup -/ pi /sup -/ inclusive correlations. (31 refs).

  13. Functional integral for non-Lagrangian systems

    CERN Document Server

    Kochan, Denis

    2010-01-01

    A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\\kappa[\\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.

  14. A generalized integral fluctuation theorem for general jump processes

    International Nuclear Information System (INIS)

    Liu Fei; Ouyang Zhongcan; Luo Yupin; Huang Mingchang

    2009-01-01

    Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem. (fast track communication)

  15. Breaking from binaries - using a sequential mixed methods design.

    Science.gov (United States)

    Larkin, Patricia Mary; Begley, Cecily Marion; Devane, Declan

    2014-03-01

    To outline the traditional worldviews of healthcare research and discuss the benefits and challenges of using mixed methods approaches in contributing to the development of nursing and midwifery knowledge. There has been much debate about the contribution of mixed methods research to nursing and midwifery knowledge in recent years. A sequential exploratory design is used as an exemplar of a mixed methods approach. The study discussed used a combination of focus-group interviews and a quantitative instrument to obtain a fuller understanding of women's experiences of childbirth. In the mixed methods study example, qualitative data were analysed using thematic analysis and quantitative data using regression analysis. Polarised debates about the veracity, philosophical integrity and motivation for conducting mixed methods research have largely abated. A mixed methods approach can contribute to a deeper, more contextual understanding of a variety of subjects and experiences; as a result, it furthers knowledge that can be used in clinical practice. The purpose of the research study should be the main instigator when choosing from an array of mixed methods research designs. Mixed methods research offers a variety of models that can augment investigative capabilities and provide richer data than can a discrete method alone. This paper offers an example of an exploratory, sequential approach to investigating women's childbirth experiences. A clear framework for the conduct and integration of the different phases of the mixed methods research process is provided. This approach can be used by practitioners and policy makers to improve practice.

  16. Employees’ Perceptions of Corporate Social Responsibility and Job Performance: A Sequential Mediation Model

    Directory of Open Access Journals (Sweden)

    Inyong Shin

    2016-05-01

    Full Text Available In spite of the increasing importance of corporate social responsibility (CSR and employee job performance, little is still known about the links between the socially responsible actions of organizations and the job performance of their members. In order to explain how employees’ perceptions of CSR influence their job performance, this study first examines the relationships between perceived CSR, organizational identification, job satisfaction, and job performance, and then develops a sequential mediation model by fully integrating these links. The results of structural equation modeling analyses conducted for 250 employees at hotels in South Korea offered strong support for the proposed model. We found that perceived CSR was indirectly and positively associated with job performance sequentially mediated first through organizational identification and then job satisfaction. This study theoretically contributes to the CSR literature by revealing the sequential mechanism through which employees’ perceptions of CSR affect their job performance, and offers practical implications by stressing the importance of employees’ perceptions of CSR. Limitations of this study and future research directions are discussed.

  17. Uniform product formulae with application to the Feynman-Nelson integral for open systems

    International Nuclear Information System (INIS)

    Exner, P.; Kolerov, G.I.

    1982-01-01

    The product formula for perturbations of propagators by Faris is generalized: we show that one can use arbitrary partitions of a given interval and perform the limit uniformly with respect to the partition norm. The results are applied to express solutions of the Schroedinger equation, in particular for some complex and time-dependent potentials, by means of Nelson-type path integrals. (orig.)

  18. Feynman-α technique for measurement of detector dead time using a 30 kW tank-in-pool research reactor

    International Nuclear Information System (INIS)

    Akaho, E.H.K.; Intsiful, J.D.K.; Maakuu, B.T.; Anim-Sampong, S.; Nyarko, B.J.B.

    2002-01-01

    Reactor noise analysis was carried out for Ghana Research Reactor-1 GHARR-1, a tank-in-pool type reactor using the Feynman-α technique (variance-to-mean method). Measurements made at different detector positions and under subcritical conditions showed that the technique could not be used to determine the prompt decay constant for the reactor which is Be reflected with photo-neutron background. However, for very low dwell times the technique was used to measure the dead time of the detector which compares favourably with the value obtained using the α-conventional method

  19. Feynman-alpha technique for measurement of detector dead time using a 30 kW tank-in-pool research reactor

    CERN Document Server

    Akaho, E H K; Intsiful, J D K; Maakuu, B T; Nyarko, B J B

    2002-01-01

    Reactor noise analysis was carried out for Ghana Research Reactor-1 GHARR-1, a tank-in-pool type reactor using the Feynman-alpha technique (variance-to-mean method). Measurements made at different detector positions and under subcritical conditions showed that the technique could not be used to determine the prompt decay constant for the reactor which is Be reflected with photo-neutron background. However, for very low dwell times the technique was used to measure the dead time of the detector which compares favourably with the value obtained using the alpha-conventional method.

  20. Sequential Generalized Transforms on Function Space

    Directory of Open Access Journals (Sweden)

    Jae Gil Choi

    2013-01-01

    Full Text Available We define two sequential transforms on a function space Ca,b[0,T] induced by generalized Brownian motion process. We then establish the existence of the sequential transforms for functionals in a Banach algebra of functionals on Ca,b[0,T]. We also establish that any one of these transforms acts like an inverse transform of the other transform. Finally, we give some remarks about certain relations between our sequential transforms and other well-known transforms on Ca,b[0,T].

  1. Modeling eye gaze patterns in clinician-patient interaction with lag sequential analysis.

    Science.gov (United States)

    Montague, Enid; Xu, Jie; Chen, Ping-Yu; Asan, Onur; Barrett, Bruce P; Chewning, Betty

    2011-10-01

    The aim of this study was to examine whether lag sequential analysis could be used to describe eye gaze orientation between clinicians and patients in the medical encounter. This topic is particularly important as new technologies are implemented into multiuser health care settings in which trust is critical and nonverbal cues are integral to achieving trust. This analysis method could lead to design guidelines for technologies and more effective assessments of interventions. Nonverbal communication patterns are important aspects of clinician-patient interactions and may affect patient outcomes. The eye gaze behaviors of clinicians and patients in 110 videotaped medical encounters were analyzed using the lag sequential method to identify significant behavior sequences. Lag sequential analysis included both event-based lag and time-based lag. Results from event-based lag analysis showed that the patient's gaze followed that of the clinician, whereas the clinician's gaze did not follow the patient's. Time-based sequential analysis showed that responses from the patient usually occurred within 2 s after the initial behavior of the clinician. Our data suggest that the clinician's gaze significantly affects the medical encounter but that the converse is not true. Findings from this research have implications for the design of clinical work systems and modeling interactions. Similar research methods could be used to identify different behavior patterns in clinical settings (physical layout, technology, etc.) to facilitate and evaluate clinical work system designs.

  2. Assessing sequential data assimilation techniques for integrating GRACE data into a hydrological model

    KAUST Repository

    Khaki, M.

    2017-07-06

    The time-variable terrestrial water storage (TWS) products from the Gravity Recovery And Climate Experiment (GRACE) have been increasingly used in recent years to improve the simulation of hydrological models by applying data assimilation techniques. In this study, for the first time, we assess the performance of the most popular data assimilation sequential techniques for integrating GRACE TWS into the World-Wide Water Resources Assessment (W3RA) model. We implement and test stochastic and deterministic ensemble-based Kalman filters (EnKF), as well as Particle filters (PF) using two different resampling approaches of Multinomial Resampling and Systematic Resampling. These choices provide various opportunities for weighting observations and model simulations during the assimilation and also accounting for error distributions. Particularly, the deterministic EnKF is tested to avoid perturbing observations before assimilation (that is the case in an ordinary EnKF). Gaussian-based random updates in the EnKF approaches likely do not fully represent the statistical properties of the model simulations and TWS observations. Therefore, the fully non-Gaussian PF is also applied to estimate more realistic updates. Monthly GRACE TWS are assimilated into W3RA covering the entire Australia. To evaluate the filters performances and analyze their impact on model simulations, their estimates are validated by independent in-situ measurements. Our results indicate that all implemented filters improve the estimation of water storage simulations of W3RA. The best results are obtained using two versions of deterministic EnKF, i.e. the Square Root Analysis (SQRA) scheme and the Ensemble Square Root Filter (EnSRF), respectively improving the model groundwater estimations errors by 34% and 31% compared to a model run without assimilation. Applying the PF along with Systematic Resampling successfully decreases the model estimation error by 23%.

  3. Forced Sequence Sequential Decoding

    DEFF Research Database (Denmark)

    Jensen, Ole Riis; Paaske, Erik

    1998-01-01

    We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low...... as Eb/N0=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since...... the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported...

  4. Sequential probability ratio controllers for safeguards radiation monitors

    International Nuclear Information System (INIS)

    Fehlau, P.E.; Coop, K.L.; Nixon, K.V.

    1984-01-01

    Sequential hypothesis tests applied to nuclear safeguards accounting methods make the methods more sensitive to detecting diversion. The sequential tests also improve transient signal detection in safeguards radiation monitors. This paper describes three microprocessor control units with sequential probability-ratio tests for detecting transient increases in radiation intensity. The control units are designed for three specific applications: low-intensity monitoring with Poisson probability ratios, higher intensity gamma-ray monitoring where fixed counting intervals are shortened by sequential testing, and monitoring moving traffic where the sequential technique responds to variable-duration signals. The fixed-interval controller shortens a customary 50-s monitoring time to an average of 18 s, making the monitoring delay less bothersome. The controller for monitoring moving vehicles benefits from the sequential technique by maintaining more than half its sensitivity when the normal passage speed doubles

  5. Bioremediation of PAHs contaminated river sediment by an integrated approach with sequential injection of co-substrate and electron acceptor: Lab-scale study.

    Science.gov (United States)

    Liu, Tongzhou; Zhang, Zhen; Dong, Wenyi; Wu, Xiaojing; Wang, Hongjie

    2017-11-01

    In this study, the feasibility of employing an integrated bioremediation approach in contaminated river sediment was evaluated. Sequential addition of co-substrate (acetate) and electron acceptor (NO 3 - ) in a two-phase treatment was capable of effectively removing polycyclic aromatic hydrocarbons (PAHs) in river sediment. The residual concentration of total PAHs decreased to far below effect range low (ERL) value within 91 days of incubation, at which concentration it could rarely pose biological impairment. The biodegradation of high molecular weight PAHs were found to be mainly occurred in the sediment treated with co-substrates (i.e. acetate or methanol), in which acetate was found to be more suitable for PAHs degradation. The role of co-substrates in influencing PAHs biodegradation was tentatively discussed herein. Additionally, the sediment odorous problem and blackish appearance were intensively addressed by NO 3 - injection. The results of this study demonstrated that integrating two or more approaches/processes would be a helpful option in sediment remediation. It can lead to a more effective remediation performance, handle multiple contamination issues, as well as mitigate environmental risks caused by one of the single methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

  6. A semi-classical treatment of dissipative processes based on Feynman's influence functional method

    International Nuclear Information System (INIS)

    Moehring, K.; Smilansky, U.

    1980-01-01

    We develop a semi-classical treatment of dissipative processes based on Feynman's influence functional method. Applying it to deep inelastic collisions of heavy ions we study inclusive transition probabilities corresponding to a situation when only a set of collective variables is specified in the initial and final states. We show that the inclusive probabilities as well as the final energy distributions can be expressed in terms of properly defined classical paths and their corresponding stability fields. We present a uniform approximation for the study of quantal interference and focussing phenomena and discuss the conditions under which they are to be expected. For the dissipation mechanism we study three approximations - the harmonic model for the internal system, the weak coupling (diabatic) and the adiabatic coupling. We show that these three limits can be treated in the same manner. We finally compare the present formalism with other methodes as were introduced for the description of dissipation in deep inelastic collisions. (orig.)

  7. Biased lineups: sequential presentation reduces the problem.

    Science.gov (United States)

    Lindsay, R C; Lea, J A; Nosworthy, G J; Fulford, J A; Hector, J; LeVan, V; Seabrook, C

    1991-12-01

    Biased lineups have been shown to increase significantly false, but not correct, identification rates (Lindsay, Wallbridge, & Drennan, 1987; Lindsay & Wells, 1980; Malpass & Devine, 1981). Lindsay and Wells (1985) found that sequential lineup presentation reduced false identification rates, presumably by reducing reliance on relative judgment processes. Five staged-crime experiments were conducted to examine the effect of lineup biases and sequential presentation on eyewitness recognition accuracy. Sequential lineup presentation significantly reduced false identification rates from fair lineups as well as from lineups biased with regard to foil similarity, instructions, or witness attire, and from lineups biased in all of these ways. The results support recommendations that police present lineups sequentially.

  8. Lineup composition, suspect position, and the sequential lineup advantage.

    Science.gov (United States)

    Carlson, Curt A; Gronlund, Scott D; Clark, Steven E

    2008-06-01

    N. M. Steblay, J. Dysart, S. Fulero, and R. C. L. Lindsay (2001) argued that sequential lineups reduce the likelihood of mistaken eyewitness identification. Experiment 1 replicated the design of R. C. L. Lindsay and G. L. Wells (1985), the first study to show the sequential lineup advantage. However, the innocent suspect was chosen at a lower rate in the simultaneous lineup, and no sequential lineup advantage was found. This led the authors to hypothesize that protection from a sequential lineup might emerge only when an innocent suspect stands out from the other lineup members. In Experiment 2, participants viewed a simultaneous or sequential lineup with either the guilty suspect or 1 of 3 innocent suspects. Lineup fairness was varied to influence the degree to which a suspect stood out. A sequential lineup advantage was found only for the unfair lineups. Additional analyses of suspect position in the sequential lineups showed an increase in the diagnosticity of suspect identifications as the suspect was placed later in the sequential lineup. These results suggest that the sequential lineup advantage is dependent on lineup composition and suspect position. (c) 2008 APA, all rights reserved

  9. Nonperturbative path integral expansion II

    International Nuclear Information System (INIS)

    Kaiser, H.J.

    1976-05-01

    The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)

  10. Tradable permit allocations and sequential choice

    Energy Technology Data Exchange (ETDEWEB)

    MacKenzie, Ian A. [Centre for Economic Research, ETH Zuerich, Zurichbergstrasse 18, 8092 Zuerich (Switzerland)

    2011-01-15

    This paper investigates initial allocation choices in an international tradable pollution permit market. For two sovereign governments, we compare allocation choices that are either simultaneously or sequentially announced. We show sequential allocation announcements result in higher (lower) aggregate emissions when announcements are strategic substitutes (complements). Whether allocation announcements are strategic substitutes or complements depends on the relationship between the follower's damage function and governments' abatement costs. When the marginal damage function is relatively steep (flat), allocation announcements are strategic substitutes (complements). For quadratic abatement costs and damages, sequential announcements provide a higher level of aggregate emissions. (author)

  11. Assets and liabilities are the momentum of particles and antiparticles displayed in Feynman-graphs

    Science.gov (United States)

    Braun, Dieter

    2001-02-01

    An analogy between assets and liabilities and the momentum of particles and antiparticles (called actons and passons) is proposed. It allows physicists to use physical methods in economy for the analysis of monetary systems and for the analysis of double entry bookkeeping. Economists can use it to subdivide and discuss complicated balance transactions in terms of Feynman-graphs which introduce the time dimension to bookkeeping. Within the analogy, assets and liabilities come into existence by pair creation. Conservation of momentum is fulfilled whereas the conservation of energy corresponds to the regulation of a constant amount of money. Interest rates accelerate the particles by imposing a negative friction. The statistical description of an ideal money gas is derived and the transcription to semiconductor physics is given. The analogy is hoped to open a new field for physics and to reveal new insights on monetary systems.

  12. Applying the minimax principle to sequential mastery testing

    NARCIS (Netherlands)

    Vos, Hendrik J.

    2002-01-01

    The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master, a nonmaster, or to continue sampling and administering another random item. The framework of minimax sequential decision theory (minimum

  13. Evaluation of variational approximations

    International Nuclear Information System (INIS)

    Trevisan, L.A.

    1991-01-01

    In Feynman's approach to quantum statistical mechanics, the partition function can e represented as a path integral. A recently proposed variation method of Feynman-Kleinert is able to transform the path integral into an integral in phase space, in which the quantum fluctuations have been taken care of by introducing the effective classical potential. This method has been testes with succeed for the smooth potentials and for the singular potential of delta. The method to the strong singular potentials is applied: a quadratic potential and a linear potential both with a rigid wall at the origin. By satisfying the condition that the density of the particle be vanish at the origin, and adapted method of Feynman-Kleinert in order to improve the method is introduced. (author)

  14. Classical and sequential limit analysis revisited

    Science.gov (United States)

    Leblond, Jean-Baptiste; Kondo, Djimédo; Morin, Léo; Remmal, Almahdi

    2018-04-01

    Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic-plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity - in the absence of hardening and within a linearized geometrical framework -, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity - although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic-plastic coupling in the specific case considered.

  15. Feynman perturbation expansion for the price of coupon bond options and swaptions in quantum finance. I. Theory.

    Science.gov (United States)

    Baaquie, Belal E

    2007-01-01

    European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.

  16. Simultaneous versus sequential penetrating keratoplasty and cataract surgery.

    Science.gov (United States)

    Hayashi, Ken; Hayashi, Hideyuki

    2006-10-01

    To compare the surgical outcomes of simultaneous penetrating keratoplasty and cataract surgery with those of sequential surgery. Thirty-nine eyes of 39 patients scheduled for simultaneous keratoplasty and cataract surgery and 23 eyes of 23 patients scheduled for sequential keratoplasty and secondary phacoemulsification surgery were recruited. Refractive error, regular and irregular corneal astigmatism determined by Fourier analysis, and endothelial cell loss were studied at 1 week and 3, 6, and 12 months after combined surgery in the simultaneous surgery group or after subsequent phacoemulsification surgery in the sequential surgery group. At 3 and more months after surgery, mean refractive error was significantly greater in the simultaneous surgery group than in the sequential surgery group, although no difference was seen at 1 week. The refractive error at 12 months was within 2 D of that targeted in 15 eyes (39%) in the simultaneous surgery group and within 2 D in 16 eyes (70%) in the sequential surgery group; the incidence was significantly greater in the sequential group (P = 0.0344). The regular and irregular astigmatism was not significantly different between the groups at 3 and more months after surgery. No significant difference was also found in the percentage of endothelial cell loss between the groups. Although corneal astigmatism and endothelial cell loss were not different, refractive error from target refraction was greater after simultaneous keratoplasty and cataract surgery than after sequential surgery, indicating a better outcome after sequential surgery than after simultaneous surgery.

  17. Online Sequential Projection Vector Machine with Adaptive Data Mean Update.

    Science.gov (United States)

    Chen, Lin; Jia, Ji-Ting; Zhang, Qiong; Deng, Wan-Yu; Wei, Wei

    2016-01-01

    We propose a simple online learning algorithm especial for high-dimensional data. The algorithm is referred to as online sequential projection vector machine (OSPVM) which derives from projection vector machine and can learn from data in one-by-one or chunk-by-chunk mode. In OSPVM, data centering, dimension reduction, and neural network training are integrated seamlessly. In particular, the model parameters including (1) the projection vectors for dimension reduction, (2) the input weights, biases, and output weights, and (3) the number of hidden nodes can be updated simultaneously. Moreover, only one parameter, the number of hidden nodes, needs to be determined manually, and this makes it easy for use in real applications. Performance comparison was made on various high-dimensional classification problems for OSPVM against other fast online algorithms including budgeted stochastic gradient descent (BSGD) approach, adaptive multihyperplane machine (AMM), primal estimated subgradient solver (Pegasos), online sequential extreme learning machine (OSELM), and SVD + OSELM (feature selection based on SVD is performed before OSELM). The results obtained demonstrated the superior generalization performance and efficiency of the OSPVM.

  18. Online Sequential Projection Vector Machine with Adaptive Data Mean Update

    Directory of Open Access Journals (Sweden)

    Lin Chen

    2016-01-01

    Full Text Available We propose a simple online learning algorithm especial for high-dimensional data. The algorithm is referred to as online sequential projection vector machine (OSPVM which derives from projection vector machine and can learn from data in one-by-one or chunk-by-chunk mode. In OSPVM, data centering, dimension reduction, and neural network training are integrated seamlessly. In particular, the model parameters including (1 the projection vectors for dimension reduction, (2 the input weights, biases, and output weights, and (3 the number of hidden nodes can be updated simultaneously. Moreover, only one parameter, the number of hidden nodes, needs to be determined manually, and this makes it easy for use in real applications. Performance comparison was made on various high-dimensional classification problems for OSPVM against other fast online algorithms including budgeted stochastic gradient descent (BSGD approach, adaptive multihyperplane machine (AMM, primal estimated subgradient solver (Pegasos, online sequential extreme learning machine (OSELM, and SVD + OSELM (feature selection based on SVD is performed before OSELM. The results obtained demonstrated the superior generalization performance and efficiency of the OSPVM.

  19. Trial Sequential Methods for Meta-Analysis

    Science.gov (United States)

    Kulinskaya, Elena; Wood, John

    2014-01-01

    Statistical methods for sequential meta-analysis have applications also for the design of new trials. Existing methods are based on group sequential methods developed for single trials and start with the calculation of a required information size. This works satisfactorily within the framework of fixed effects meta-analysis, but conceptual…

  20. Sequentially pulsed traveling wave accelerator

    Science.gov (United States)

    Caporaso, George J [Livermore, CA; Nelson, Scott D [Patterson, CA; Poole, Brian R [Tracy, CA

    2009-08-18

    A sequentially pulsed traveling wave compact accelerator having two or more pulse forming lines each with a switch for producing a short acceleration pulse along a short length of a beam tube, and a trigger mechanism for sequentially triggering the switches so that a traveling axial electric field is produced along the beam tube in synchronism with an axially traversing pulsed beam of charged particles to serially impart energy to the particle beam.

  1. Quantum walks in brain microtubules--a biomolecular basis for quantum cognition?

    Science.gov (United States)

    Hameroff, Stuart

    2014-01-01

    Cognitive decisions are best described by quantum mathematics. Do quantum information devices operate in the brain? What would they look like? Fuss and Navarro () describe quantum lattice registers in which quantum superpositioned pathways interact (compute/integrate) as 'quantum walks' akin to Feynman's path integral in a lattice (e.g. the 'Feynman quantum chessboard'). Simultaneous alternate pathways eventually reduce (collapse), selecting one particular pathway in a cognitive decision, or choice. This paper describes how quantum walks in a Feynman chessboard are conceptually identical to 'topological qubits' in brain neuronal microtubules, as described in the Penrose-Hameroff 'Orch OR' theory of consciousness. Copyright © 2013 Cognitive Science Society, Inc.

  2. An Efficient System Based On Closed Sequential Patterns for Web Recommendations

    OpenAIRE

    Utpala Niranjan; R.B.V. Subramanyam; V-Khana

    2010-01-01

    Sequential pattern mining, since its introduction has received considerable attention among the researchers with broad applications. The sequential pattern algorithms generally face problems when mining long sequential patterns or while using very low support threshold. One possible solution of such problems is by mining the closed sequential patterns, which is a condensed representation of sequential patterns. Recently, several researchers have utilized the sequential pattern discovery for d...

  3. Intensity modulated radiotherapy with simultaneous integrated boost vs. conventional radiotherapy with sequential boost for breast cancer - A preliminary result.

    Science.gov (United States)

    Lee, Hsin-Hua; Hou, Ming-Feng; Chuang, Hung-Yi; Huang, Ming-Yii; Tsuei, Le-Ping; Chen, Fang-Ming; Ou-Yang, Fu; Huang, Chih-Jen

    2015-10-01

    This study was aimed to assess the acute dermatological adverse effect from two distinct RT techniques for breast cancer patients. We compared intensity-modulated radiotherapy with simultaneous integrated boost (IMRT-SIB) and conventional radiotherapy followed by sequential boost (CRT-SB). The study population was composed of 126 consecutive female breast cancer patients treated with breast conserving surgery. Sixty-six patients received IMRT-SIB to 2 dose levels simultaneously. They received 50.4 Gy at 1.8 Gy per fraction to the whole breast and 60.2 Gy at 2.15 Gy per fraction to the tumor bed by integral boost. Sixty patients in the CRT-SB group received 50 Gy in 25 fractions to the whole breast followed by a boost irradiation to tumor bed in 5-7 fractions to a total dose of 60-64 Gy. Acute skin toxicities were documented in agreement with the Common Terminology Criteria for Adverse Events version 3 (CTCAE v.3.0). Ninety-eight patients had grade 1 radiation dermatitis while 14 patients had grade 2. Among those with grade 2, there were 3 patients in IMRT-SIB group (4.5%) while 11 in CRT-SB group (18.3%). (P = 0.048) There was no patient with higher than grade 2 toxicity. Three year local control was 99.2%, 3-year disease free survival was 97.5% and 3-year overall survival was 99.2%. A significant reduction in the severity of acute radiation dermatitis from IMRT-SIB comparing with CRT-SB is demonstrated. Copyright © 2015 Elsevier Ltd. All rights reserved.

  4. Field theory

    CERN Multimedia

    1999-11-08

    In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

  5. Challenges and opportunities in integration of design and control

    DEFF Research Database (Denmark)

    Huusom, Jakob Kjøbsted

    2015-01-01

    Process synthesis and design of plant operation are related topics but current industrial practice solves these problems sequentially. The implication of this sequential strategy may result in design of processing systems which are very hard to control. This paper presents a discussion on drivers...... for an integrated approach and outlines the challenges in formulation of such a multi-objective synthesis problem. This discussion is viewed in relation to some of the changing trends in the industry. Significant results have been published which in different ways seek to handle the integrated problem. Further...

  6. The economic, environmental and public health impacts of new power plants: a sequential inter industry model integrated with GIS data

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, Andre F.T.; Hewings, Geoffrey J.D.; Guilhoto, Joaquim J.M. [Universidade de Sao Paulo (FEA/USP), SE (Brazil). Fac. de Administracao e Contabilidade

    2010-07-01

    The electrical sector is responsible for a considerable amount of greenhouse gases emissions worldwide, but also the one in which modern society depends the most for maintenance of quality of life as well as the functioning of economic and social activities. Invariably, even CO2 emission-free power plants have some indirect environmental impacts due to the economic effects they produce during their life cycle (construction, O and M and decommissioning). Thus, sustainability issues should be always considered in energy planning, by evaluating the balance of positive/negative externalities on different areas of the country. This study aims to introduce a social-environmental economic model, based on a Regional Sequential Inter industry Model (SIM) integrated with geoprocessing data, in order to identify economic, pollution and public health impacts in state level for energy planning analysis. The model is based on the Impact Pathway Approach Methodology, using geoprocessing to locate social-environmental variables for dispersion and health evaluations. The final goal is to provide an auxiliary tool for policy makers to assess energy planning scenarios in Brazil. (author)

  7. The mapping approach in the path integral formalism applied to curve-crossing systems

    International Nuclear Information System (INIS)

    Novikov, Alexey; Kleinekathoefer, Ulrich; Schreiber, Michael

    2004-01-01

    The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath consisting of harmonic oscillators. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the generating functional for the electronic trajectories. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate within a perturbative treatment for a small coordinate shift between the potential energy surfaces

  8. On the presentation of wave phenomena of electrons with the Young-Feynman experiment

    International Nuclear Information System (INIS)

    Matteucci, Giorgio

    2011-01-01

    The Young-Feynman two-hole interferometer is widely used to present electron wave-particle duality and, in particular, the buildup of interference fringes with single electrons. The teaching approach consists of two steps: (i) electrons come through only one hole but diffraction effects are disregarded and (ii) electrons come through both holes and interference fringes are described. Therefore, a student might believe that wave phenomena are not revealed in case (i), but they arise only by the combined effect of electrons from the two holes. To avoid misunderstanding regarding the distribution of electrons passing through one hole, Fresnel and Fraunhofer diffraction patterns are discussed. In particular, an original experiment, realized with a standard electron microscope and a sample with round holes, is presented to introduce the wave nature of electrons. The experimental results clearly show that a careful discussion of electron diffraction phenomena from one hole provides students with the evidence that the interference experiment from both holes is not strictly required to show the superposition of electron waves.

  9. An integrated technique using zero-valent iron and UV/H2O2 sequential process for complete decolorization and mineralization of C.I. Acid Black 24 wastewater

    International Nuclear Information System (INIS)

    Chang, M.-C.; Shu, H.-Y.; Yu, H.-H.

    2006-01-01

    The zero-valent iron (ZVI) reduction succeeds for decolorization, while UV/H 2 O 2 oxidation process results into mineralization, so that this study proposed an integrated technique by reduction coupling with oxidation process in order to acquire simultaneously complete both decolorization and mineralization of C.I. Acid Black 24. From the experimental data, the zero-valent iron addition alone can decolorize the dye wastewater yet it demanded longer time than ZVI coupled with UV/H 2 O 2 processes (Red-Ox). Moreover, it resulted into only about 30% removal of the total organic carbon (TOC), which was capable to be effectively mineralized by UV/H 2 O 2 process. The proposed sequential ZVI-UV/H 2 O 2 integration system cannot only effectively remove color and TOC in AB 24 wastewater simultaneously but also save irradiation power and time demand. Furthermore, the decolorization rate constants were about 3.77-4.0 times magnitude comparing with that by UV/H 2 O 2 process alone

  10. Discrimination between sequential and simultaneous virtual channels with electrical hearing.

    Science.gov (United States)

    Landsberger, David; Galvin, John J

    2011-09-01

    In cochlear implants (CIs), simultaneous or sequential stimulation of adjacent electrodes can produce intermediate pitch percepts between those of the component electrodes. However, it is unclear whether simultaneous and sequential virtual channels (VCs) can be discriminated. In this study, CI users were asked to discriminate simultaneous and sequential VCs; discrimination was measured for monopolar (MP) and bipolar + 1 stimulation (BP + 1), i.e., relatively broad and focused stimulation modes. For sequential VCs, the interpulse interval (IPI) varied between 0.0 and 1.8 ms. All stimuli were presented at comfortably loud, loudness-balanced levels at a 250 pulse per second per electrode (ppse) stimulation rate. On average, CI subjects were able to reliably discriminate between sequential and simultaneous VCs. While there was no significant effect of IPI or stimulation mode on VC discrimination, some subjects exhibited better VC discrimination with BP + 1 stimulation. Subjects' discrimination between sequential and simultaneous VCs was correlated with electrode discrimination, suggesting that spatial selectivity may influence perception of sequential VCs. To maintain equal loudness, sequential VC amplitudes were nearly double those of simultaneous VCs, presumably resulting in a broader spread of excitation. These results suggest that perceptual differences between simultaneous and sequential VCs might be explained by differences in the spread of excitation. © 2011 Acoustical Society of America

  11. Sequential versus simultaneous market delineation

    DEFF Research Database (Denmark)

    Haldrup, Niels; Møllgaard, Peter; Kastberg Nielsen, Claus

    2005-01-01

    and geographical markets. Using a unique data setfor prices of Norwegian and Scottish salmon, we propose a methodologyfor simultaneous market delineation and we demonstrate that comparedto a sequential approach conclusions will be reversed.JEL: C3, K21, L41, Q22Keywords: Relevant market, econometric delineation......Delineation of the relevant market forms a pivotal part of most antitrustcases. The standard approach is sequential. First the product marketis delineated, then the geographical market is defined. Demand andsupply substitution in both the product dimension and the geographicaldimension...

  12. The effect of the vertical part of the path on the real time Feynman rules in finite temperature field theory 2-point functions and vacuum diagrams

    International Nuclear Information System (INIS)

    Gelis, F.

    1996-01-01

    The effect of the contribution of the vertical part of the real time path is studied completely in the case of two points functions and vacuum diagrams. Indeed, this vertical part generally contributes in the calculation of a given graph. Moreover, this contribution is essential in order to have a consistent equilibrium theory: thanks to this contribution, the Green functions are effectively invariant by time translation, as they should be. As a by product, it is shown that the perturbative calculations give a result which does not depend on the initial time t I and final time t F of the path. The property of independence with respect to t I is closely related to the KMS conditions, i.e. to the fact the system is in thermal equilibrium. In the case of two point functions and vacuum diagrams, the contribution of the vertical part can be taken into account by the n(vertical stroke k 0 vertical stroke) prescription in the usual RTF Feynman rules. The extra Feynman rule needed for vacuum diagrams is shown not to be related directly to the contribution of the vertical part of the path. (orig.). With 4 figs

  13. Achieving Integration in Mixed Methods Designs—Principles and Practices

    Science.gov (United States)

    Fetters, Michael D; Curry, Leslie A; Creswell, John W

    2013-01-01

    Mixed methods research offers powerful tools for investigating complex processes and systems in health and health care. This article describes integration principles and practices at three levels in mixed methods research and provides illustrative examples. Integration at the study design level occurs through three basic mixed method designs—exploratory sequential, explanatory sequential, and convergent—and through four advanced frameworks—multistage, intervention, case study, and participatory. Integration at the methods level occurs through four approaches. In connecting, one database links to the other through sampling. With building, one database informs the data collection approach of the other. When merging, the two databases are brought together for analysis. With embedding, data collection and analysis link at multiple points. Integration at the interpretation and reporting level occurs through narrative, data transformation, and joint display. The fit of integration describes the extent the qualitative and quantitative findings cohere. Understanding these principles and practices of integration can help health services researchers leverage the strengths of mixed methods. PMID:24279835

  14. α′-Expansion of open string disk integrals via Mellin transformations

    Directory of Open Access Journals (Sweden)

    Ellis Ye Yuan

    2015-02-01

    Full Text Available Open string disk integrals are represented as contour integrals of a product of Beta functions using Mellin transformations. This makes the mathematical problem of computing the α′-expansion around the field-theory limit similar to that of the ϵ-expansion in Feynman loop integrals around the four-dimensional limit. More explicitly, the formula in Mellin space obtained directly from the standard Koba–Nielsen-like representation is valid in a region of values of α′ that does not include α′=0. Analytic continuation is therefore needed since contours are pinched by poles as α′→0. Deforming contours that get pinched by poles generates a set of (n−3! multi-dimensional residues left behind which contain all the field theory information. Some analogies between the field theory formulas obtained by this method and those derived recently from using the scattering equations are commented at the end.

  15. Group-sequential analysis may allow for early trial termination

    DEFF Research Database (Denmark)

    Gerke, Oke; Vilstrup, Mie H; Halekoh, Ulrich

    2017-01-01

    BACKGROUND: Group-sequential testing is widely used in pivotal therapeutic, but rarely in diagnostic research, although it may save studies, time, and costs. The purpose of this paper was to demonstrate a group-sequential analysis strategy in an intra-observer study on quantitative FDG-PET/CT mea......BACKGROUND: Group-sequential testing is widely used in pivotal therapeutic, but rarely in diagnostic research, although it may save studies, time, and costs. The purpose of this paper was to demonstrate a group-sequential analysis strategy in an intra-observer study on quantitative FDG...

  16. Sequential logic analysis and synthesis

    CERN Document Server

    Cavanagh, Joseph

    2007-01-01

    Until now, there was no single resource for actual digital system design. Using both basic and advanced concepts, Sequential Logic: Analysis and Synthesis offers a thorough exposition of the analysis and synthesis of both synchronous and asynchronous sequential machines. With 25 years of experience in designing computing equipment, the author stresses the practical design of state machines. He clearly delineates each step of the structured and rigorous design principles that can be applied to practical applications. The book begins by reviewing the analysis of combinatorial logic and Boolean a

  17. Dosimetric comparison of the related parameters between simultaneous integrated boost intensity-modulated radiotherapy and sequential boost conformal radiotherapy for postoperative malignant glioma of the brain

    International Nuclear Information System (INIS)

    Shao Qian; Lu Jie; Li Jianbin; Sun Tao; Bai Tong; Liu Tonghai; Yin Yong

    2011-01-01

    Objective: To compare the dosimetric of different parameter of simultaneous integrated boost intensity-modulated radiotherapy (SIB-IMRT) with sequential boost conformal radiotherapy (SB-CRT) for postoperative malignant glioma of the brain. Methods: Ten patients with malignant glioma of brain were selected to study. Each patient was simulated all by CT and MRI, and the imagings of CT and MRI were all sent to Pinnacle 3 planning system. The fusion technology with MR-CT imaging was used on Pinnacle 3 planning system. The target volume was delineated and defined based on MRI. The postoperative residual lesion and resection cavity were defined as gross tumor volume (GTV) and expanded GTV some scope was defined as clinical target volume (CTV). The margins of GTV expanded 10 mm and 25 mm were defined as CTV1 and CTV2 respectively. CTV1 and CTV2 all enlarged 5 mm were defined as PTV1 and PTV2 respectively. The plans of simultaneous integrated boost intensity-modulated radiotherapy and sequential boost conformal radiotherapy were respectively designed for each patient using Pinnacle 3 planning system and the dosimetric of different parameter was compared. The prescribe dose of SIB-IMRT was PTV1: 62.5 Gy/25 f, PTV2: 50.0 Gy/25 f; and SB-CRT was PTV1: 66.0 Gy/33 f, PTV2: 50.0 Gy/25 f. The dosimetries of different parameters of SIB-IMRT and SB-CRT were compared by using Paired-Samples T Test. Results: The maximum and mean dose of PTV1, PTV2, and brainstem were of significant difference (P 0.05). Conclusion: The SIB-IMRT plan is better than the SB-CRT plan. The CI and HI of SIB-IMRT are superior to SB-CRT. At the same time, it can preserve the important organs such as brainstem and reduce the mean dose of whole brain. On the other hand it can shorten the total period of therapy time. (authors)

  18. Structural Consistency, Consistency, and Sequential Rationality.

    OpenAIRE

    Kreps, David M; Ramey, Garey

    1987-01-01

    Sequential equilibria comprise consistent beliefs and a sequentially ra tional strategy profile. Consistent beliefs are limits of Bayes ratio nal beliefs for sequences of strategies that approach the equilibrium strategy. Beliefs are structurally consistent if they are rationaliz ed by some single conjecture concerning opponents' strategies. Consis tent beliefs are not necessarily structurally consistent, notwithstan ding a claim by Kreps and Robert Wilson (1982). Moreover, the spirit of stru...

  19. Use of helicity methods in evaluating loop integrals: a QCD example

    International Nuclear Information System (INIS)

    Koerner, J.G.; Sieben, P.

    1991-01-01

    We discuss the use of helicity methods in evaluating loop diagrams by analyzing a specific example: the one-loop concentration to e + e - → qanti qg in massless QCD. By using covariant helicity representations for the spinor and vector wave functins we obtain the helicity amplitudes directly from the Feynman loop diagrams by covariant contraction. The necessary loop integrations are considerably simplified since one encounters only scalar loop integrals after contraction. We discuss crossing relations that allow one to obtain the corresponding one-loop helicity amplitudes for the crossed processes as e.g. qanti q → (W, Z, γ * ) + g including the real photon cases. As we treat the spin degrees of freedom in four dimensions and only continue momenta to n dimensions (dimensional reduction scheme) we explicate how our results are related to the usual dimensional regularization results. (orig.)

  20. Generalized infimum and sequential product of quantum effects

    International Nuclear Information System (INIS)

    Li Yuan; Sun Xiuhong; Chen Zhengli

    2007-01-01

    The quantum effects for a physical system can be described by the set E(H) of positive operators on a complex Hilbert space H that are bounded above by the identity operator I. For A, B(set-membership sign)E(H), the operation of sequential product A(convolution sign)B=A 1/2 BA 1/2 was proposed as a model for sequential quantum measurements. A nice investigation of properties of the sequential product has been carried over [Gudder, S. and Nagy, G., 'Sequential quantum measurements', J. Math. Phys. 42, 5212 (2001)]. In this note, we extend some results of this reference. In particular, a gap in the proof of Theorem 3.2 in this reference is overcome. In addition, some properties of generalized infimum A sqcap B are studied

  1. Short-Range Temporal Interactions in Sleep; Hippocampal Spike Avalanches Support a Large Milieu of Sequential Activity Including Replay.

    Directory of Open Access Journals (Sweden)

    J Matthew Mahoney

    Full Text Available Hippocampal neural systems consolidate multiple complex behaviors into memory. However, the temporal structure of neural firing supporting complex memory consolidation is unknown. Replay of hippocampal place cells during sleep supports the view that a simple repetitive behavior modifies sleep firing dynamics, but does not explain how multiple episodes could be integrated into associative networks for recollection during future cognition. Here we decode sequential firing structure within spike avalanches of all pyramidal cells recorded in sleeping rats after running in a circular track. We find that short sequences that combine into multiple long sequences capture the majority of the sequential structure during sleep, including replay of hippocampal place cells. The ensemble, however, is not optimized for maximally producing the behavior-enriched episode. Thus behavioral programming of sequential correlations occurs at the level of short-range interactions, not whole behavioral sequences and these short sequences are assembled into a large and complex milieu that could support complex memory consolidation.

  2. When good is stickier than bad: Understanding gain/loss asymmetries in sequential framing effects.

    Science.gov (United States)

    Sparks, Jehan; Ledgerwood, Alison

    2017-08-01

    Considerable research has demonstrated the power of the current positive or negative frame to shape people's current judgments. But humans must often learn about positive and negative information as they encounter that information sequentially over time. It is therefore crucial to consider the potential importance of sequencing when developing an understanding of how humans think about valenced information. Indeed, recent work looking at sequentially encountered frames suggests that some frames can linger outside the context in which they are first encountered, sticking in the mind so that subsequent frames have a muted effect. The present research builds a comprehensive account of sequential framing effects in both the loss and the gain domains. After seeing information about a potential gain or loss framed in positive terms or negative terms, participants saw the same issue reframed in the opposing way. Across 5 studies and 1566 participants, we find accumulating evidence for the notion that in the gain domain, positive frames are stickier than negative frames for novel but not familiar scenarios, whereas in the loss domain, negative frames are always stickier than positive frames. Integrating regulatory focus theory with the literatures on negativity dominance and positivity offset, we develop a new and comprehensive account of sequential framing effects that emphasizes the adaptive value of positivity and negativity biases in specific contexts. Our findings highlight the fact that research conducted solely in the loss domain risks painting an incomplete and oversimplified picture of human bias and suggest new directions for future research. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  3. Sequential analysis in neonatal research-systematic review.

    Science.gov (United States)

    Lava, Sebastiano A G; Elie, Valéry; Ha, Phuong Thi Viet; Jacqz-Aigrain, Evelyne

    2018-05-01

    As more new drugs are discovered, traditional designs come at their limits. Ten years after the adoption of the European Paediatric Regulation, we performed a systematic review on the US National Library of Medicine and Excerpta Medica database of sequential trials involving newborns. Out of 326 identified scientific reports, 21 trials were included. They enrolled 2832 patients, of whom 2099 were analyzed: the median number of neonates included per trial was 48 (IQR 22-87), median gestational age was 28.7 (IQR 27.9-30.9) weeks. Eighteen trials used sequential techniques to determine sample size, while 3 used continual reassessment methods for dose-finding. In 16 studies reporting sufficient data, the sequential design allowed to non-significantly reduce the number of enrolled neonates by a median of 24 (31%) patients (IQR - 4.75 to 136.5, p = 0.0674) with respect to a traditional trial. When the number of neonates finally included in the analysis was considered, the difference became significant: 35 (57%) patients (IQR 10 to 136.5, p = 0.0033). Sequential trial designs have not been frequently used in Neonatology. They might potentially be able to reduce the number of patients in drug trials, although this is not always the case. What is known: • In evaluating rare diseases in fragile populations, traditional designs come at their limits. About 20% of pediatric trials are discontinued, mainly because of recruitment problems. What is new: • Sequential trials involving newborns were infrequently used and only a few (n = 21) are available for analysis. • The sequential design allowed to non-significantly reduce the number of enrolled neonates by a median of 24 (31%) patients (IQR - 4.75 to 136.5, p = 0.0674).

  4. Evaluation of a novel PTFE material for separation and preconcentration of trace levels of metal ions in sequential injection (SI) and sequential injection lab-on-valve (SI-LOV) systems interfaced with detection by ETAAS

    DEFF Research Database (Denmark)

    Long, Xiangbao; Chomchoei, Roongrat; Gała, Piotr

    The operational characteristics of a novel PTFE bead material, granular Algoflon®, used for separation and preconcentration of metal ions via adsorption of on-line generated non-charged metal complexes, were evaluated in a sequential injection (SI) system furnished with an external packed column...... and in a sequential injection lab-on-valve (SI-LOV) system. Employed for the determination of cadmium(II), complexed with diethyldithiophosphate (DDPA), and detection by electrothermal atomic absorption spectrometry (ETAAS), its performance was compared to that of a previously used material, Aldrich PTFE, which had...... demonstrated that PTFE was the most promising for solid-state pretreatments. By comparing the two materials, the Algoflon® beads exhibited much higher sensitivity (1.6107 versus 0.2956 μg l-1 per integrated absorbance (s)), and better retention efficiency (82% versus 74%) and enrichment factor (20.8 versus 17...

  5. Group-sequential analysis may allow for early trial termination

    DEFF Research Database (Denmark)

    Gerke, Oke; Vilstrup, Mie H; Halekoh, Ulrich

    2017-01-01

    BACKGROUND: Group-sequential testing is widely used in pivotal therapeutic, but rarely in diagnostic research, although it may save studies, time, and costs. The purpose of this paper was to demonstrate a group-sequential analysis strategy in an intra-observer study on quantitative FDG-PET/CT mea......BACKGROUND: Group-sequential testing is widely used in pivotal therapeutic, but rarely in diagnostic research, although it may save studies, time, and costs. The purpose of this paper was to demonstrate a group-sequential analysis strategy in an intra-observer study on quantitative FDG...... assumed to be normally distributed, and sequential one-sided hypothesis tests on the population standard deviation of the differences against a hypothesised value of 1.5 were performed, employing an alpha spending function. The fixed-sample analysis (N = 45) was compared with the group-sequential analysis...... strategies comprising one (at N = 23), two (at N = 15, 30), or three interim analyses (at N = 11, 23, 34), respectively, which were defined post hoc. RESULTS: When performing interim analyses with one third and two thirds of patients, sufficient agreement could be concluded after the first interim analysis...

  6. Audio-visual speech perception in prelingually deafened Japanese children following sequential bilateral cochlear implantation.

    Science.gov (United States)

    Yamamoto, Ryosuke; Naito, Yasushi; Tona, Risa; Moroto, Saburo; Tamaya, Rinko; Fujiwara, Keizo; Shinohara, Shogo; Takebayashi, Shinji; Kikuchi, Masahiro; Michida, Tetsuhiko

    2017-11-01

    An effect of audio-visual (AV) integration is observed when the auditory and visual stimuli are incongruent (the McGurk effect). In general, AV integration is helpful especially in subjects wearing hearing aids or cochlear implants (CIs). However, the influence of AV integration on spoken word recognition in individuals with bilateral CIs (Bi-CIs) has not been fully investigated so far. In this study, we investigated AV integration in children with Bi-CIs. The study sample included thirty one prelingually deafened children who underwent sequential bilateral cochlear implantation. We assessed their responses to congruent and incongruent AV stimuli with three CI-listening modes: only the 1st CI, only the 2nd CI, and Bi-CIs. The responses were assessed in the whole group as well as in two sub-groups: a proficient group (syllable intelligibility ≥80% with the 1st CI) and a non-proficient group (syllable intelligibility effect in each of the three CI-listening modes. AV integration responses were observed in a subset of incongruent AV stimuli, and the patterns observed with the 1st CI and with Bi-CIs were similar. In the proficient group, the responses with the 2nd CI were not significantly different from those with the 1st CI whereas in the non-proficient group the responses with the 2nd CI were driven by visual stimuli more than those with the 1st CI. Our results suggested that prelingually deafened Japanese children who underwent sequential bilateral cochlear implantation exhibit AV integration abilities, both in monaural listening as well as in binaural listening. We also observed a higher influence of visual stimuli on speech perception with the 2nd CI in the non-proficient group, suggesting that Bi-CIs listeners with poorer speech recognition rely on visual information more compared to the proficient subjects to compensate for poorer auditory input. Nevertheless, poorer quality auditory input with the 2nd CI did not interfere with AV integration with binaural

  7. Comparison of ablation centration after bilateral sequential versus simultaneous LASIK.

    Science.gov (United States)

    Lin, Jane-Ming; Tsai, Yi-Yu

    2005-01-01

    To compare ablation centration after bilateral sequential and simultaneous myopic LASIK. A retrospective randomized case series was performed of 670 eyes of 335 consecutive patients who had undergone either bilateral sequential (group 1) or simultaneous (group 2) myopic LASIK between July 2000 and July 2001 at the China Medical University Hospital, Taichung, Taiwan. The ablation centrations of the first and second eyes in the two groups were compared 3 months postoperatively. Of 670 eyes, 274 eyes (137 patients) comprised the sequential group and 396 eyes (198 patients) comprised the simultaneous group. Three months post-operatively, 220 eyes of 110 patients (80%) in the sequential group and 236 eyes of 118 patients (60%) in the simultaneous group provided topographic data for centration analysis. For the first eyes, mean decentration was 0.39 +/- 0.26 mm in the sequential group and 0.41 +/- 0.19 mm in the simultaneous group (P = .30). For the second eyes, mean decentration was 0.28 +/- 0.23 mm in the sequential group and 0.30 +/- 0.21 mm in the simultaneous group (P = .36). Decentration in the second eyes significantly improved in both groups (group 1, P = .02; group 2, P sequential group and 0.32 +/- 0.18 mm in the simultaneous group (P = .33). The difference of ablation center angles between the first and second eyes was 43.2 sequential group and 45.1 +/- 50.8 degrees in the simultaneous group (P = .42). Simultaneous bilateral LASIK is comparable to sequential surgery in ablation centration.

  8. Algorithms to solve coupled systems of differential equations in terms of power series

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Schneider, Carsten

    2016-08-01

    Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations, and that sufficiently many initial values of the integrals are given. Then there exist algorithms that decide constructively if the coefficients of their power series representations can be given within the class of nested sums over hypergeometric products. In this article we work out the calculation steps that solve this problem. First, we present a successful tactic that has been applied recently to challenging problems coming from massive 3-loop Feynman integrals. Here our main tool is to solve scalar linear recurrences within the class of nested sums over hypergeometric products. Second, we will present a new variation of this tactic which relies on more involved summation technologies but succeeds in reducing the problem to solve scalar recurrences with lower recurrence orders. The article works out the different challenges of this new tactic and demonstrates how they can be treated efficiently with our existing summation technologies.

  9. A Survey of Multi-Objective Sequential Decision-Making

    NARCIS (Netherlands)

    Roijers, D.M.; Vamplew, P.; Whiteson, S.; Dazeley, R.

    2013-01-01

    Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential

  10. Scalar one-loop integrals using the negative-dimension approach

    International Nuclear Information System (INIS)

    Anastasiou, C.; Glover, E.W.N.; Oleari, C.

    2000-01-01

    We study massive one-loop integrals by analytically continuing the Feynman integral to negative dimensions as advocated by Halliday and Ricotta and developed by Suzuki and Schmidt. We consider n-point one-loop integrals with arbitrary powers of propagators in general dimension D. For integrals with m mass scales and q external momentum scales, we construct a template solution valid for all n which allows us to obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with m+q-1 variables. All solutions for all possible kinematic regions are given simultaneously, allowing the investigation of different ranges of variation of mass and momentum scales. As a first step, we develop the general framework and apply it to massive bubble and vertex integrals. Of course many of these integrals are well known and we show that the known results are recovered. To give a concrete new result, we present expressions for the general vertex integral with one off-shell leg and two internal masses in terms of hypergeometric functions of two variables that converge in the appropriate kinematic regions. The kinematic singularity structure of this graph is sufficiently complex to give insight into how the negative-dimension method operates and gives some hope that more complicated graphs can also be evaluated

  11. Sequential lineups: shift in criterion or decision strategy?

    Science.gov (United States)

    Gronlund, Scott D

    2004-04-01

    R. C. L. Lindsay and G. L. Wells (1985) argued that a sequential lineup enhanced discriminability because it elicited use of an absolute decision strategy. E. B. Ebbesen and H. D. Flowe (2002) argued that a sequential lineup led witnesses to adopt a more conservative response criterion, thereby affecting bias, not discriminability. Height was encoded as absolute (e.g., 6 ft [1.83 m] tall) or relative (e.g., taller than). If a sequential lineup elicited an absolute decision strategy, the principle of transfer-appropriate processing predicted that performance should be best when height was encoded absolutely. Conversely, if a simultaneous lineup elicited a relative decision strategy, performance should be best when height was encoded relatively. The predicted interaction was observed, providing direct evidence for the decision strategies explanation of what happens when witnesses view a sequential lineup.

  12. Gluing Ladder Feynman Diagrams into Fishnets

    International Nuclear Information System (INIS)

    Basso, Benjamin; Dixon, Lance J.; Stanford University, CA; University of California, Santa Barbara, CA

    2017-01-01

    We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ "4 theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

  13. Improving the variational path integral approach to the quantum double-well potential

    International Nuclear Information System (INIS)

    Bao Jingdong; Wang Hongyu

    2002-01-01

    An improved variational path integral approach is developed and applied to the quantum double-well potential, in which part of the quartic term of the potential is included in the trial action. The expression of the effective classical potential (ECP) under a non-Gaussian expectation is obtained. Here the frequency and fourth-order derivative of the potential are treated as two variational parameters, determined by the minimization of the ECP at each point. We calculate the ECP, the free energy and the level splitting of a symmetrical double-well potential. It is shown that the present results are better than those of the Feynman-Kleinert Gaussian variational method. (author)

  14. Achieving integration in mixed methods designs-principles and practices.

    Science.gov (United States)

    Fetters, Michael D; Curry, Leslie A; Creswell, John W

    2013-12-01

    Mixed methods research offers powerful tools for investigating complex processes and systems in health and health care. This article describes integration principles and practices at three levels in mixed methods research and provides illustrative examples. Integration at the study design level occurs through three basic mixed method designs-exploratory sequential, explanatory sequential, and convergent-and through four advanced frameworks-multistage, intervention, case study, and participatory. Integration at the methods level occurs through four approaches. In connecting, one database links to the other through sampling. With building, one database informs the data collection approach of the other. When merging, the two databases are brought together for analysis. With embedding, data collection and analysis link at multiple points. Integration at the interpretation and reporting level occurs through narrative, data transformation, and joint display. The fit of integration describes the extent the qualitative and quantitative findings cohere. Understanding these principles and practices of integration can help health services researchers leverage the strengths of mixed methods. © Health Research and Educational Trust.

  15. How to Read the Tractatus Sequentially

    Directory of Open Access Journals (Sweden)

    Tim Kraft

    2016-11-01

    Full Text Available One of the unconventional features of Wittgenstein’s Tractatus Logico-Philosophicus is its use of an elaborated and detailed numbering system. Recently, Bazzocchi, Hacker und Kuusela have argued that the numbering system means that the Tractatus must be read and interpreted not as a sequentially ordered book, but as a text with a two-dimensional, tree-like structure. Apart from being able to explain how the Tractatus was composed, the tree reading allegedly solves exegetical issues both on the local (e. g. how 4.02 fits into the series of remarks surrounding it and the global level (e. g. relation between ontology and picture theory, solipsism and the eye analogy, resolute and irresolute readings. This paper defends the sequential reading against the tree reading. After presenting the challenges generated by the numbering system and the two accounts as attempts to solve them, it is argued that Wittgenstein’s own explanation of the numbering system, anaphoric references within the Tractatus and the exegetical issues mentioned above do not favour the tree reading, but a version of the sequential reading. This reading maintains that the remarks of the Tractatus form a sequential chain: The role of the numbers is to indicate how remarks on different levels are interconnected to form a concise, surveyable and unified whole.

  16. A minimax procedure in the context of sequential mastery testing

    NARCIS (Netherlands)

    Vos, Hendrik J.

    1999-01-01

    The purpose of this paper is to derive optimal rules for sequential mastery tests. In a sequential mastery test, the decision is to classify a subject as a master or a nonmaster, or to continue sampling and administering another random test item. The framework of minimax sequential decision theory

  17. Multichannel, sequential or combined X-ray spectrometry

    International Nuclear Information System (INIS)

    Florestan, J.

    1979-01-01

    X-ray spectrometer qualities and defects are evaluated for sequential and multichannel categories. Multichannel X-ray spectrometer has time-coherency advantage and its results could be more reproducible; on the other hand some spatial incoherency limits low percentage and traces applications, specially when backgrounds are very variable. In this last case, sequential X-ray spectrometer would find again great usefulness [fr

  18. Calculations in perturbative string field theory

    International Nuclear Information System (INIS)

    Thorn, C.B.

    1987-01-01

    The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules

  19. Induction of simultaneous and sequential malolactic fermentation in durian wine.

    Science.gov (United States)

    Taniasuri, Fransisca; Lee, Pin-Rou; Liu, Shao-Quan

    2016-08-02

    This study represented for the first time the impact of malolactic fermentation (MLF) induced by Oenococcus oeni and its inoculation strategies (simultaneous vs. sequential) on the fermentation performance as well as aroma compound profile of durian wine. There was no negative impact of simultaneous inoculation of O. oeni and Saccharomyces cerevisiae on the growth and fermentation kinetics of S. cerevisiae as compared to sequential fermentation. Simultaneous MLF did not lead to an excessive increase in volatile acidity as compared to sequential MLF. The kinetic changes of organic acids (i.e. malic, lactic, succinic, acetic and α-ketoglutaric acids) varied with simultaneous and sequential MLF relative to yeast alone. MLF, regardless of inoculation mode, resulted in higher production of fermentation-derived volatiles as compared to control (alcoholic fermentation only), including esters, volatile fatty acids, and terpenes, except for higher alcohols. Most indigenous volatile sulphur compounds in durian were decreased to trace levels with little differences among the control, simultaneous and sequential MLF. Among the different wines, the wine with simultaneous MLF had higher concentrations of terpenes and acetate esters while sequential MLF had increased concentrations of medium- and long-chain ethyl esters. Relative to alcoholic fermentation only, both simultaneous and sequential MLF reduced acetaldehyde substantially with sequential MLF being more effective. These findings illustrate that MLF is an effective and novel way of modulating the volatile and aroma compound profile of durian wine. Copyright © 2016 Elsevier B.V. All rights reserved.

  20. Kinetic parameters of the GUINEVERE reference configuration in VENUS-F reactor obtained from a pile noise experiment using Rossi and Feynman methods

    Energy Technology Data Exchange (ETDEWEB)

    Geslot, Benoit; Pepino, Alexandra; Blaise, Patrick; Mellier, Frederic [CEA, DEN, DER/SPEx, Cadarache, F-13108 St Paul Lez Durance (France); Lecouey, Jean-Luc [LPC Caen, ENSICAEN, Universite de Caen, CNRS/IN2P3, 6 Bd. Marechal Juin 14050 Caen cedex (France); Carta, Mario [ENEA, UTFISST-REANUC, C.R. Casaccia, S.P.040 via Anguillarese 301, 00123 S. Maria Di Galeria, Roma (Italy); Kochetkov, Anatoly; Vittiglio, Guido [SCK.CEN, Belgian Nuclear Research Centre, Boeretang 200, BE-2400, Mol (Belgium); Billebaud, Annick [LPSC, CNRS, IN2P3/UJF/INPG, 53 Avenue des Martyrs, 38026 Grenoble cedex (France)

    2015-07-01

    A pile noise measurement campaign has been conducted by the CEA in the VENUS-F reactor (SCK-CEN, Mol Belgium) in April 2011 in the reference critical configuration of the GUINEVERE experimental program. The experimental setup made it possible to estimate the core kinetic parameters: the prompt neutron decay constant, the delayed neutron fraction and the generation time. A precise assessment of these constants is of prime importance. In particular, the effective delayed neutron fraction is used to normalize and compare calculated reactivities of different subcritical configurations, obtained by modifying either the core layout or the control rods position, with experimental ones deduced from the analysis of measurements. This paper presents results obtained with a CEA-developed time stamping acquisition system. Data were analyzed using Rossi-α and Feynman-α methods. Results were normalized to reactor power using a calibrated fission chamber with a deposit of Np-237. Calculated factors were necessary to the analysis: the Diven factor was computed by the ENEA (Italy) and the power calibration factor by the CNRS/IN2P3/LPC Caen. Results deduced with both methods are consistent with respect to calculated quantities. Recommended values are given by the Rossi-α estimator, that was found to be the most robust. The neutron generation time was found equal to 0.438 ± 0.009 μs and the effective delayed neutron fraction is 765 ± 8 pcm. Discrepancies with the calculated value (722 pcm, calculation from ENEA) are satisfactory: -5.6% for the Rossi-α estimate and -2.7% for the Feynman-α estimate. (authors)