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.
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.
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.
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.)
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.)
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.)
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.
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
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.
Analytic Tools for Feynman Integrals
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...
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
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
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.)
Feynman Integrals with Absorbing Boundaries
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 ...
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.)
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
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
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.)
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.
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
Feynman integrals in QCD made simple
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.
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
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
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.
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.
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.
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.
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
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
The algebraic locus of Feynman integrals
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...
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)
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)
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.)
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
Probing finite coarse-grained virtual Feynman histories with sequential weak values
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.
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
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.
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.
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
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.)
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
Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.
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.
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.)
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)
Mathematical theory of Feynman path integrals an introduction
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.
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
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.)
Rigorous time slicing approach to Feynman path integrals
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...
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
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.
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.
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
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
Picard-Fuchs equations of dimensionally regulated Feynman integrals
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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
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
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.
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
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
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.
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)
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.
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.)
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.)
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.)
arXiv Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
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...
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.)
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
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.
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.
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.)
The ε-form of the differential equations for Feynman integrals in the elliptic case
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.
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.)
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)
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.)
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.)
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.
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
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
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.)
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
Systematic approximation of multi-scale Feynman integrals arXiv
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.
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
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
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
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.)
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
Solving differential equations for Feynman integrals by expansions near singular points
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.
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
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.)
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.
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.
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
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...
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.)
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.)
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.)
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)
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
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.
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.
Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral
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...
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.
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...
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
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.
Transforming differential equations of multi-loop Feynman integrals into canonical form
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.
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.
Regularizing Feynman path integrals using the generalized Kontsevich-Vishik trace
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.
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.)
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…
Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form
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
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.)
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.)
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.
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
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
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
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
Professor Richard Feynman colloquium
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.
Feynman Lectures on Computation
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,"
Introduction to Feynman diagrams
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
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.
Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
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.
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
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.
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.
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)
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.)
Reverse Engineering Camouflaged Sequential Integrated Circuits Without Scan Access
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...
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
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)
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.
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.
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
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)
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 ...
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).
Quantum Man: Richard Feynman's Life in Science
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.
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
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
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)
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)
Sequential circuit design for radiation hardened multiple voltage integrated circuits
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.
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)
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
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.
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.)
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....
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.
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.
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
Feynman's operational calculus and beyond noncommutativity and time-ordering
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...
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
Perturbation theory via Feynman diagrams in classical mechanics
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.
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.
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.
FeynRules - Feynman rules made easy
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...
Detailed balance of the Feynman micromotor
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.
Feynman propagator for spin foam quantum gravity.
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".
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
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)
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.
Constructive Representation Theory for the Feynman Operator Calculus
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...
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.)
Richard Feynman Quarks, Bombs, and Bongos
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
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.)
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
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.
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 ...
Vous voulez rire, monsieur Feynman !
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.
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.)
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
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
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.)
(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.
Simultaneous integrated vs. sequential boost in VMAT radiotherapy of high-grade gliomas.
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.
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%.
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
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.)
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
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
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....
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
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
Spin wave Feynman diagram vertex computation package
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.
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-.
Simultaneous integrated vs. sequential boost in VMAT radiotherapy of high-grade gliomas
Energy Technology Data Exchange (ETDEWEB)
Farzin, Mostafa [Klinikum rechts der Isar, Technische Universitaet Muenchen, Department of Radiation Oncology, Munich (Germany); Tehran University of Medical Science, Brain and Spinal Cord Injury Research Center, Neuroscience Institute, Tehran (Iran, Islamic Republic of); Molls, Michael; Astner, Sabrina; Oechsner, Markus [Klinikum rechts der Isar, Technische Universitaet Muenchen, Department of Radiation Oncology, Munich (Germany); Rondak, Ina-Christine [Klinikum rechts der Isar, Technische Universitaet Muenchen, Institut fuer Medizinische Statistik und Epidemiologie, Munich (Germany)
2015-12-15
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 (D{sub max} and D{sub mean}) 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. (orig.) [German] Es wurden 2 Arten der Planung fuer die volumetrisch modulierte Rotationsbestrahlung (VMAT) bei 20 Patienten mit hochgradigen Gliomen verglichen: simultan integrierter Boost (SIB) und sequenzieller Boost (SEB). Dazu wurde die Dosisverteilung in den Zielvolumina und den Risikoorganen analysiert. Es wurden Planungsvolumina (PTV), Boostvolumina (BV) und Risikoorgane konturiert sowie SIB- und SEB-Plaene erstellt. Der SEB besteht aus 2 Plaenen. Im ersten Plan erhaelt das PTV 50 Gy in 25 Fraktionen. Im zweiten Plan erhaelt das Boostvolumen 10 Gy in 5 Fraktionen (Einzeldosis jeweils 2 Gy). Die Dosis
Huygens-Feynman-Fresnel principle as the basis of applied optics.
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.
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
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
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
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.
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.
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.
Richard Feynman a life in science
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.
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
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.).
Le cours de physique de Feynman
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.
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
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''
Directory of Open Access Journals (Sweden)
Timothy L Haskett
2018-03-01
Full Text Available Tripartite integrative and conjugative elements (ICE3 are a novel form of ICE that exist as three separate DNA regions integrated within the genomes of Mesorhizobium spp. Prior to conjugative transfer the three ICE3 regions of M. ciceri WSM1271 ICEMcSym1271 combine and excise to form a single circular element. This assembly requires three coordinated recombination events involving three site-specific recombinases IntS, IntG and IntM. Here, we demonstrate that three excisionases-or recombination directionality factors-RdfS, RdfG and RdfM are required for ICE3 excision. Transcriptome sequencing revealed that expression of ICE3 transfer and conjugation genes was induced by quorum sensing. Quorum sensing activated expression of rdfS, and in turn RdfS stimulated transcription of both rdfG and rdfM. Therefore, RdfS acts as a "master controller" of ICE3 assembly and excision. The dependence of all three excisive reactions on RdfS ensures that ICE3 excision occurs via a stepwise sequence of recombination events that avoids splitting the chromosome into a non-viable configuration. These discoveries expose a surprisingly simple control system guiding molecular assembly of these novel and complex mobile genetic elements and highlight the diverse and critical functions of excisionase proteins in control of horizontal gene transfer.
Haskett, Timothy L; Terpolilli, Jason J; Ramachandran, Vinoy K; Verdonk, Callum J; Poole, Phillip S; O'Hara, Graham W; Ramsay, Joshua P
2018-03-01
Tripartite integrative and conjugative elements (ICE3) are a novel form of ICE that exist as three separate DNA regions integrated within the genomes of Mesorhizobium spp. Prior to conjugative transfer the three ICE3 regions of M. ciceri WSM1271 ICEMcSym1271 combine and excise to form a single circular element. This assembly requires three coordinated recombination events involving three site-specific recombinases IntS, IntG and IntM. Here, we demonstrate that three excisionases-or recombination directionality factors-RdfS, RdfG and RdfM are required for ICE3 excision. Transcriptome sequencing revealed that expression of ICE3 transfer and conjugation genes was induced by quorum sensing. Quorum sensing activated expression of rdfS, and in turn RdfS stimulated transcription of both rdfG and rdfM. Therefore, RdfS acts as a "master controller" of ICE3 assembly and excision. The dependence of all three excisive reactions on RdfS ensures that ICE3 excision occurs via a stepwise sequence of recombination events that avoids splitting the chromosome into a non-viable configuration. These discoveries expose a surprisingly simple control system guiding molecular assembly of these novel and complex mobile genetic elements and highlight the diverse and critical functions of excisionase proteins in control of horizontal gene transfer.
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.)
Counting the number of Feynman graphs in QCD
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.
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.
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
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)
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.
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
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.)
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)
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.)
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)
Miyazaki, Masayoshi; Nishiyama, Kinji; Ueda, Yoshihiro; Ohira, Shingo; Tsujii, Katsutomo; Isono, Masaru; Masaoka, Akira; Teshima, Teruki
2016-07-01
The aim of this study was to compare three strategies for intensity-modulated radiotherapy (IMRT) for 20 head-and-neck cancer patients. For simultaneous integrated boost (SIB), doses were 66 and 54 Gy in 30 fractions for PTVboost and PTVelective, respectively. Two-phase IMRT delivered 50 Gy in 25 fractions to PTVelective in the First Plan, and 20 Gy in 10 fractions to PTVboost in the Second Plan. Sequential SIB (SEQ-SIB) delivered 55 Gy and 50 Gy in 25 fractions, respectively, to PTVboost and PTVelective using SIB in the First Plan and 11 Gy in 5 fractions to PTVboost in the Second Plan. Conformity indexes (CIs) (mean ± SD) for PTVboost and PTVelective were 1.09 ± 0.05 and 1.34 ± 0.12 for SIB, 1.39 ± 0.14 and 1.80 ± 0.28 for two-phase IMRT, and 1.14 ± 0.07 and 1.60 ± 0.18 for SEQ-SIB, respectively. CI was significantly highest for two-phase IMRT. Maximum doses (Dmax) to the spinal cord were 42.1 ± 1.5 Gy for SIB, 43.9 ± 1.0 Gy for two-phase IMRT and 40.3 ± 1.8 Gy for SEQ-SIB. Brainstem Dmax were 50.1 ± 2.2 Gy for SIB, 50.5 ± 4.6 Gy for two-phase IMRT and 47.4 ± 3.6 Gy for SEQ-SIB. Spinal cord Dmax for the three techniques was significantly different, and brainstem Dmax was significantly lower for SEQ-SIB. The compromised conformity of two-phase IMRT can result in higher doses to organs at risk (OARs). Lower OAR doses in SEQ-SIB made SEQ-SIB an alternative to SIB, which applies unconventional doses per fraction. © The Author 2016. Published by Oxford University Press on behalf of The Japan Radiation Research Society and Japanese Society for Radiation Oncology.
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
Quantum leap from Dirac and Feynman, across the universe, to human body and mind
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
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.)
Analytic properties of Feynman diagrams in quantum field theory
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
Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism
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.
Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism
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.
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.
Exact Maximum-Entropy Estimation with Feynman Diagrams
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.
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.)
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.
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.
Bizer, David S; DeMarzo, Peter M
1992-01-01
The authors study environments in which agents may borrow sequentially from more than one leader. Although debt is prioritized, additional lending imposes an externality on prior debt because, with moral hazard, the probability of repayment of prior loans decreases. Equilibrium interest rates are higher than they would be if borrowers could commit to borrow from at most one bank. Even though the loan terms are less favorable than they would be under commitment, the indebtedness of borrowers i...
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.
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
Poisson processes on groups and Feynman path integrals
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.
1979-09-01
An expression is given for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems
Feynman path integral in area tensor Regge calculus and positivity
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2004-01-01
The versions of quantum measure in the area tensor Regge calculus constructed in the previous paper are studied on the simplest configurations of the system. These are found to be positively defined in the Euclidean case on physical surface corresponding to the ordinary Regge calculus (but not outside this surface), that is, adopt probabilistic interpretation. (Since Euclidean measure is defined via analytical continuation, positivity is not evident property.) An argument for positivity on physical surface on general configurations of area tensor Regge calculus is given
Feynman rules for the Standard Model Effective Field Theory in R ξ -gauges
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.
Feynman-Kac equations for reaction and diffusion processes
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.
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.
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.
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.
Solutions of the Wheeler-Feynman equations with discontinuous velocities.
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.
Destructive interferences results in bosons anti bunching: refining Feynman's argument
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.
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
Roh, Whijae; Chen, Pei-Ling; Reuben, Alexandre; Spencer, Christine N.; Prieto, Peter A.; Miller, John P.; Gopalakrishnan, Vancheswaran; Wang, Feng; Cooper, Zachary A.; Reddy, Sangeetha M.; Gumbs, Curtis; Little, Latasha; Chang, Qing; Chen, Wei-Shen; Wani, Khalida; Petaccia De Macedo, Mariana; Chen, Eveline; Austin-Breneman, Jacob L.; Jiang, Hong; Roszik, Jason; Tetzlaff, Michael T.; Davies, Michael A.; Gershenwald, Jeffrey E.; Tawbi, Hussein; Lazar, Alexander J.; Hwu, Patrick; Hwu, Wen-Jen; Diab, Adi; Glitza, Isabella C.; Patel, Sapna P.; Woodman, Scott E.; Amaria, Rodabe N.; Prieto, Victor G.; Hu, Jianhua; Sharma, Padmanee; Allison, James P.; Chin, Lynda; Zhang, Jianhua; Wargo, Jennifer A.; Futreal, P. Andrew
2018-01-01
Immune checkpoint blockade produces clinical benefit in many patients. However better biomarkers of response are still needed, and mechanisms of resistance remain incompletely understood. To address this, we recently studied a cohort of melanoma patients treated with sequential checkpoint blockade against cytotoxic T lymphocyte antigen-4 (CTLA-4) followed by programmed death receptor-1 (PD-1), and identified immune markers of response and resistance. Building on these studies, we performed deep molecular profiling including T-cell receptor sequencing (TCR-seq) and whole exome sequencing (WES) within the same cohort, and demonstrated that a more clonal T cell repertoire was predictive of response to PD-1 but not CTLA-4 blockade. Analysis of copy number alterations identified a higher burden of copy number loss in non-responders to CTLA-4 and PD-1 blockade and found that it was associated with decreased expression of genes in immune-related pathways. The effect of mutational load and burden of copy number loss on response was non-redundant, suggesting the potential utility of a combinatorial biomarker to optimize patient care with checkpoint blockade therapy. PMID:28251903
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.
Ding, Nai; Pan, Xunyi; Luo, Cheng; Su, Naifei; Zhang, Wen; Zhang, Jianfeng
2018-01-31
How the brain groups sequential sensory events into chunks is a fundamental question in cognitive neuroscience. This study investigates whether top-down attention or specific tasks are required for the brain to apply lexical knowledge to group syllables into words. Neural responses tracking the syllabic and word rhythms of a rhythmic speech sequence were concurrently monitored using electroencephalography (EEG). The participants performed different tasks, attending to either the rhythmic speech sequence or a distractor, which was another speech stream or a nonlinguistic auditory/visual stimulus. Attention to speech, but not a lexical-meaning-related task, was required for reliable neural tracking of words, even when the distractor was a nonlinguistic stimulus presented cross-modally. Neural tracking of syllables, however, was reliably observed in all tested conditions. These results strongly suggest that neural encoding of individual auditory events (i.e., syllables) is automatic, while knowledge-based construction of temporal chunks (i.e., words) crucially relies on top-down attention. SIGNIFICANCE STATEMENT Why we cannot understand speech when not paying attention is an old question in psychology and cognitive neuroscience. Speech processing is a complex process that involves multiple stages, e.g., hearing and analyzing the speech sound, recognizing words, and combining words into phrases and sentences. The current study investigates which speech-processing stage is blocked when we do not listen carefully. We show that the brain can reliably encode syllables, basic units of speech sounds, even when we do not pay attention. Nevertheless, when distracted, the brain cannot group syllables into multisyllabic words, which are basic units for speech meaning. Therefore, the process of converting speech sound into meaning crucially relies on attention. Copyright © 2018 the authors 0270-6474/18/381178-11$15.00/0.
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.
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.
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.
Extended Hellmann-Feynman theorem for degenerate eigenstates
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.
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
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)
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.)
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
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
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
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.
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.
León-López, Liliana; Dávila-Ortiz, Gloria; Jiménez-Martínez, Cristian; Hernández-Sánchez, Humberto
2013-01-01
Jatropha curcas seed cake is a protein-rich byproduct of oil extraction which could be used to produce protein isolates. The purpose of this study was the optimization of the protein isolation process from the seed cake of an edible provenance of J. curcas by an alkaline extraction followed by isoelectric precipitation method via a sequentially integrated optimization approach. The influence of four different factors (solubilization pH, extraction temperature, NaCl addition, and precipitation pH) on the protein and antinutritional compounds content of the isolate was evaluated. The estimated optimal conditions were an extraction temperature of 20°C, a precipitation pH of 4, and an amount of NaCl in the extraction solution of 0.6 M for a predicted protein content of 93.3%. Under these conditions, it was possible to obtain experimentally a protein isolate with 93.21% of proteins, 316.5 mg 100 g(-1) of total phenolics, 2891.84 mg 100 g(-1) of phytates and 168 mg 100 g(-1) of saponins. The protein content of the this isolate was higher than the content reported by other authors.
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.
Generalized internal multiple imaging (GIMI) using Feynman-like diagrams
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.
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
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
ALOHA: Automatic libraries of helicity amplitudes for Feynman diagram computations
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
Generalized internal multiple imaging (GIMI) using Feynman-like diagrams
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.
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.)
Gravitational lensing of the CMB: A Feynman diagram approach
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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.
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
You err, Einstein.. Newton, Einstein, Heisenberg, and Feynman discuss quantum physics
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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
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.
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.
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.
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.
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.)
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.
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
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
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)
A new look at the Feynman ‘hodograph’ approach to the Kepler first law
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.
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.
Drawing theories apart the dispersion of Feynman diagrams in postwar physics
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...
International Nuclear Information System (INIS)
Watanabe, Junji; Akashi, Mitsuru
2008-01-01
Biointerfaces are crucial for regulating biofunctions. An effective method of producing new biomaterials is surface modification, in particular, the hybrid organic-inorganic approach. In this paper, we propose a method for the sequential formation of hydroxyapatite and calcium carbonate on porous polyester membranes by using an improved alternate soaking process. The resulting hybrid membranes were characterized in terms of their calcium and phosphorus ion contents; further, their structure was analyzed by scanning electron microscopy (SEM), X-ray diffraction (XRD), and infrared spectroscopy (IR). As a typical biofunction, protein adsorption by these hybrid membranes was investigated. Sequential hydroxyapatite and calcium carbonate formation on the membranes was successfully achieved, and the total amounts of hydroxyapatite and calcium carbonate formed were precisely regulated by the preparative conditions. The SEM and XRD characterizations were verified by comparing with the IR results. The amount of adsorbed protein correlated well with not only the amount of hydroxyapatite formed but also the combined amounts of hydroxyapatite and calcium carbonate formed. The results indicate that the hybrid membranes can function as high-performance biointerfaces that are capable of loading biomolecules such as proteins
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.
Energy Technology Data Exchange (ETDEWEB)
Stromberger, Carmen; Ghadjar, Pirus; Marnitz, Simone; Thieme, Alexander Henry; Jahn, Ulrich; Karaj-Rossbacher, Evis; Budach, Volker [Charite Universitaetsmedizin Berlin, Department of Radiation Oncology and Radiotherapy, Berlin (Germany); Raguse, Jan D. [Charite Universitaetsmedizin Berlin, Clinic for Oral and Maxillofacial Surgery, Berlin (Germany); Boettcher, Arne [Charite Universitaetsmedizin Berlin, Otorhinolaryngology, Berlin (Germany); Jamil, Basil [Communal Hospital Frankfurt Oder, Department of Radiation Oncology, Frankfurt/Oder (Germany)
2016-01-15
The purpose of this work was to compare sequential (SeqB) versus simultaneous integrated boost (SIB) radiotherapy plans delivered with volumetric modulated arc therapy (VMAT) for patients with locally advanced squamous cell cancer of the head and neck (HNSCC). SeqB and SIB plans using VMAT for 10 HNSCC patients given definitive chemoradiation were generated and analysed for differences in dose distribution, coverage, conformity and homogeneity to the planning target volumes (PTV) 1-3 and sparing of organs at risk (OAR). The mean delineated volumes ± standard deviations were 137.7 ± 44.8, 351.3 ± 83.9 and 895.6 ± 120.5 cm{sup 3} for PTV1-3. The mean volumes encompassed by the corresponding 95 % isodoses were 281 (+ 110 %) ± 73.4, 712.2 (+ 115 %) ± 146.4 and 1381.1 (+ 54 %) ± 217.3 cm{sup 3} with SeqB and 138.2 (+ 7 %) ± 40.1, 380.4 (+ 11 %) ± 91.9 and 1057.3 (+ 21 %) ± 161.4 cm{sup 3} with SIB for PTV1-3, respectively. Both strategies achieved excellent PTV coverage. SeqB provided significantly better coverage of PTV1 and 3, worse conformity for PTV1-3 and a higher mean dose than prescribed (111-115 %) to PTV2 and 3 (p ≤ 0.007). Both strategies provided satisfactory OAR sparing. This study showed significant dosimetric differences with potential clinical relevance between two VMAT boost strategies regarding coverage, conformity and dose to the PTVs. SIB might cause less toxicity. A clinical phase III/IV trial endorsed by the German Head and Neck Clinical Trials Group (IAG-KHT) will evaluate differences in acute/late toxicity as well as in locoregional recurrences between the two boost techniques. (orig.) [German] Vergleich von sequentiellem (SeqB) und simultan-integriertem Boost (SIB) mit moderner volumetrischer Arc-Therapie (VMAT) fuer Patienten mit Plattenepithelkarzinomen der Kopf-Hals-Region. Fuer 10 Patienten mit Plattenepithelkarzinomen der Kopf-Hals-Region und definitiver Radiochemotherapie erfolgte eine VMAT-Planung als SeqB und SIB fuer die
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)
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.
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
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
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.
Teaching Electron--Positron--Photon Interactions with Hands-on Feynman Diagrams
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…
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.)
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.))
A guide to Feynman diagrams in the many-body problem
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.
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)
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.)
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
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
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
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.
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.)
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
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)
Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane
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.
Sequential stochastic optimization
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
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
Renormalization in the complete Mellin representation of Feynman amplitudes
International Nuclear Information System (INIS)
Calan, C. de; David, F.; Rivasseau, V.
1981-01-01
The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)
Sequential memory: Binding dynamics
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.
Sequential Dependencies in Driving
Doshi, Anup; Tran, Cuong; Wilder, Matthew H.; Mozer, Michael C.; Trivedi, Mohan M.
2012-01-01
The effect of recent experience on current behavior has been studied extensively in simple laboratory tasks. We explore the nature of sequential effects in the more naturalistic setting of automobile driving. Driving is a safety-critical task in which delayed response times may have severe consequences. Using a realistic driving simulator, we find…
Mining compressing sequential problems
Hoang, T.L.; Mörchen, F.; Fradkin, D.; Calders, T.G.K.
2012-01-01
Compression based pattern mining has been successfully applied to many data mining tasks. We propose an approach based on the minimum description length principle to extract sequential patterns that compress a database of sequences well. We show that mining compressing patterns is NP-Hard and
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.)
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.
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.)
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.
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.
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)
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
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
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.
Academic Training Lecture | Beyond Feynman Diagrams (1/3) | 24 April
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 ...
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.
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...
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
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
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)
Mean field simulation for Monte Carlo integration
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
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.
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
Forced Sequence Sequential Decoding
DEFF Research Database (Denmark)
Jensen, Ole Riis
In this thesis 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 codes with non-uniform profile. With this scheme decoding with good performance...... is possible as low as Eb/No=0.6 dB, which is about 1.7 dB below the signal-to-noise ratio that marks the cut-off 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 Reed-Solomon word is decoded after C computations are presented. This is supported by simulation results that are also extended to other parameters....
Sequential Power-Dependence Theory
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
Modelling sequentially scored item responses
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
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...
DEFF Research Database (Denmark)
Hansen, Elo Harald
waste generation. Most recently, the socalled third generation of FIA has emerged, that is, the Lab-on-Valve (LOV) approach, the conceptual basis of which is to incorporate all the necessary unit operational manipulations required, and, when possible, even the detection device into a single small...... integrated microconduit, or “laboratory”, placed atop a selection valve. The lecture will detail the evolution of the three generations of FIA, emphasis being placed on the LOV approach. Proven itself as a versatile front end to a variety of detection techniques, its utility will be exemplified by a series...... of the renewable microcolumn concept. Despite their excellent analytical chemical capabilities, ETAAS as well as ICPMS often require that the samples are subjected to suitable pretreatment in order to obtain the necessary sensitivity and selectivity. Either in order to separate the analyte from potentially...
DEFF Research Database (Denmark)
Hansen, Elo Harald
waste generation. Most recently, the Lab-on-Valve (LOV) approach has emerged. Termed the third generation of FIA, the conceptual basis of the LOV is to incorporate all the necessary unit operational manipulations required in a chemical assay, and, when possible, even the detection device, into a single...... small integrated microconduit, or “laboratory”, placed atop a selection valve. In the lecture emphasis will be placed on the LOV approach. Proven itself as a versatile front end to a variety of detection techniques, its utility will be exemplified by various applications. Particular focus......-phase microcolumn concept utilising hydrophobic as well as hydrophilic bead materials. Although ETAAS and ICPMS both are characterised by excellent analytical chemical capabilities, they nevertheless often require that the samples be subjected to suitable pretreatment in order to obtain the necessary sensitivity...
The Feynman-Vernon Influence Functional Approach in QED
International Nuclear Information System (INIS)
Biryukov, Alexander; Shleenkov, Mark
2016-01-01
In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum
Loopedia, a database for loop integrals
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.
International Nuclear Information System (INIS)
Yoshida, Toshihiro
1981-01-01
Probabilities of meson production in the sequential decay of Reggeons, which are formed from the projectile and the target in the hadron-hadron to Reggeon-Reggeon processes, are investigated. It is assumed that pair creation of heavy quarks and simultaneous creation of two antiquark-quark pairs are negligible. The leading-order terms with respect to ratio of creation probabilities of anti s s to anti u u (anti d d) are calculated. The production cross sections in the target fragmentation region are given in terms of probabilities in the initial decay of the Reggeons and an effect of manyparticle production. (author)
Mathemagics (A Tribute to L. Euler and R. Feynman)
Cartier, Pierre
The implicit philosophical belief of the working mathematician is today the Hilbert-Bourbaki formalism. Ideally, one works within a closed system: the basic principles are clearly enunciated once for all, including (that is an addition of twentieth century science) the formal rules of logical reasoning clothed in mathematical form. The basic principles include precise definitions of all mathematical objects, and the coherence between the various branches of mathematical sciences is achieved through reduction to basic models in the universe of sets. A very important feature of the system is its non-contradiction ; after Gödel, we have lost the initial hopes to establish this non-contradiction by a formal reasoning, but one can live with a corresponding belief in non-contradiction. The whole structure is certainly very appealing, but the illusion is that it is eternal, that it will function for ever according to the same principles. What history of mathematics teaches us is that the principles of mathematical deduction, and not simply the mathematical theories, have evolved over the centuries. In modern times, theories like General Topology or Lebesgue's Integration Theory represent an almost perfect model of precision, flexibility and harmony, and their applications, for instance to probability theory, have been very successful.
Synthetic Aperture Sequential Beamforming
DEFF Research Database (Denmark)
Kortbek, Jacob; Jensen, Jørgen Arendt; Gammelmark, Kim Løkke
2008-01-01
A synthetic aperture focusing (SAF) technique denoted Synthetic Aperture Sequential Beamforming (SASB) suitable for 2D and 3D imaging is presented. The technique differ from prior art of SAF in the sense that SAF is performed on pre-beamformed data contrary to channel data. The objective is to im......A synthetic aperture focusing (SAF) technique denoted Synthetic Aperture Sequential Beamforming (SASB) suitable for 2D and 3D imaging is presented. The technique differ from prior art of SAF in the sense that SAF is performed on pre-beamformed data contrary to channel data. The objective...... is to improve and obtain a more range independent lateral resolution compared to conventional dynamic receive focusing (DRF) without compromising frame rate. SASB is a two-stage procedure using two separate beamformers. First a set of Bmode image lines using a single focal point in both transmit and receive...... is stored. The second stage applies the focused image lines from the first stage as input data. The SASB method has been investigated using simulations in Field II and by off-line processing of data acquired with a commercial scanner. The performance of SASB with a static image object is compared with DRF...
Songthong, Anussara P; Kannarunimit, Danita; Chakkabat, Chakkapong; Lertbutsayanukul, Chawalit
2015-08-08
To investigate acute and late toxicities comparing sequential (SEQ-IMRT) versus simultaneous integrated boost intensity modulated radiotherapy (SIB-IMRT) in nasopharyngeal carcinoma (NPC) patients. Newly diagnosed stage I-IVB NPC patients were randomized to receive SEQ-IMRT or SIB-IMRT, with or without chemotherapy. SEQ-IMRT consisted of two sequential radiation treatment plans: 2 Gy x 25 fractions to low-risk planning target volume (PTV-LR) followed by 2 Gy x 10 fractions to high-risk planning target volume (PTV-HR). In contrast, SIB-IMRT consisted of only one treatment plan: 2.12 Gy and 1.7 Gy x 33 fractions to PTV-HR and PTV-LR, respectively. Toxicities were evaluated according to CTCAE version 4.0. Between October 2010 and November 2013, 122 eligible patients were randomized between SEQ-IMRT (54 patients) and SIB-IMRT (68 patients). With median follow-up time of 16.8 months, there was no significant difference in toxicities between the two IMRT techniques. During chemoradiation, the most common grade 3-5 acute toxicities were mucositis (15.4% vs 13.6%, SEQ vs SIB, p = 0.788) followed by dysphagia (9.6% vs 9.1%, p = 1.000) and xerostomia (9.6% vs 7.6%, p = 0.748). During the adjuvant chemotherapy period, 25.6% and 32.7% experienced grade 3 weight loss in SEQ-IMRT and SIB-IMRT (p = 0.459). One-year overall survival (OS) and progression-free survival (PFS) were 95.8% and 95.5% in SEQ-IMRT and 98% and 90.2% in SIB-IMRT, respectively (p = 0.472 for OS and 0.069 for PFS). This randomized, phase II/III trial comparing SIB-IMRT versus SEQ-IMRT in NPC showed no statistically significant difference between both IMRT techniques in terms of acute adverse events. Short-term tumor control and survival outcome were promising.
International Nuclear Information System (INIS)
Songthong, Anussara P.; Kannarunimit, Danita; Chakkabat, Chakkapong; Lertbutsayanukul, Chawalit
2015-01-01
To investigate acute and late toxicities comparing sequential (SEQ-IMRT) versus simultaneous integrated boost intensity modulated radiotherapy (SIB-IMRT) in nasopharyngeal carcinoma (NPC) patients. Newly diagnosed stage I-IVB NPC patients were randomized to receive SEQ-IMRT or SIB-IMRT, with or without chemotherapy. SEQ-IMRT consisted of two sequential radiation treatment plans: 2Gy x 25 fractions to low-risk planning target volume (PTV-LR) followed by 2Gy x 10 fractions to high-risk planning target volume (PTV-HR). In contrast, SIB-IMRT consisted of only one treatment plan: 2.12Gy and 1.7Gy x 33 fractions to PTV-HR and PTV-LR, respectively. Toxicities were evaluated according to CTCAE version 4.0. Between October 2010 and November 2013, 122 eligible patients were randomized between SEQ-IMRT (54 patients) and SIB-IMRT (68 patients). With median follow-up time of 16.8 months, there was no significant difference in toxicities between the two IMRT techniques. During chemoradiation, the most common grade 3–5 acute toxicities were mucositis (15.4 % vs 13.6 %, SEQ vs SIB, p = 0.788) followed by dysphagia (9.6 % vs 9.1 %, p = 1.000) and xerostomia (9.6 % vs 7.6 %, p = 0.748). During the adjuvant chemotherapy period, 25.6 % and 32.7 % experienced grade 3 weight loss in SEQ-IMRT and SIB-IMRT (p = 0.459). One-year overall survival (OS) and progression-free survival (PFS) were 95.8 % and 95.5 % in SEQ-IMRT and 98 % and 90.2 % in SIB-IMRT, respectively (p = 0.472 for OS and 0.069 for PFS). This randomized, phase II/III trial comparing SIB-IMRT versus SEQ-IMRT in NPC showed no statistically significant difference between both IMRT techniques in terms of acute adverse events. Short-term tumor control and survival outcome were promising
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.
Properties of the Feynman-alpha method applied to accelerator-driven subcritical systems.
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.
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
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.)
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
JaxoDraw: A graphical user interface for drawing Feynman diagrams
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
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)
Path Integration on the Upper Half-Plane
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.
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
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
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.
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
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.)
Adaptive sequential controller
Energy Technology Data Exchange (ETDEWEB)
El-Sharkawi, Mohamed A. (Renton, WA); Xing, Jian (Seattle, WA); Butler, Nicholas G. (Newberg, OR); Rodriguez, Alonso (Pasadena, CA)
1994-01-01
An adaptive sequential controller (50/50') for controlling a circuit breaker (52) or other switching device to substantially eliminate transients on a distribution line caused by closing and opening the circuit breaker. The device adaptively compensates for changes in the response time of the circuit breaker due to aging and environmental effects. A potential transformer (70) provides a reference signal corresponding to the zero crossing of the voltage waveform, and a phase shift comparator circuit (96) compares the reference signal to the time at which any transient was produced when the circuit breaker closed, producing a signal indicative of the adaptive adjustment that should be made. Similarly, in controlling the opening of the circuit breaker, a current transformer (88) provides a reference signal that is compared against the time at which any transient is detected when the circuit breaker last opened. An adaptive adjustment circuit (102) produces a compensation time that is appropriately modified to account for changes in the circuit breaker response, including the effect of ambient conditions and aging. When next opened or closed, the circuit breaker is activated at an appropriately compensated time, so that it closes when the voltage crosses zero and opens when the current crosses zero, minimizing any transients on the distribution line. Phase angle can be used to control the opening of the circuit breaker relative to the reference signal provided by the potential transformer.
Adaptive sequential controller
El-Sharkawi, Mohamed A.; Xing, Jian; Butler, Nicholas G.; Rodriguez, Alonso
1994-01-01
An adaptive sequential controller (50/50') for controlling a circuit breaker (52) or other switching device to substantially eliminate transients on a distribution line caused by closing and opening the circuit breaker. The device adaptively compensates for changes in the response time of the circuit breaker due to aging and environmental effects. A potential transformer (70) provides a reference signal corresponding to the zero crossing of the voltage waveform, and a phase shift comparator circuit (96) compares the reference signal to the time at which any transient was produced when the circuit breaker closed, producing a signal indicative of the adaptive adjustment that should be made. Similarly, in controlling the opening of the circuit breaker, a current transformer (88) provides a reference signal that is compared against the time at which any transient is detected when the circuit breaker last opened. An adaptive adjustment circuit (102) produces a compensation time that is appropriately modified to account for changes in the circuit breaker response, including the effect of ambient conditions and aging. When next opened or closed, the circuit breaker is activated at an appropriately compensated time, so that it closes when the voltage crosses zero and opens when the current crosses zero, minimizing any transients on the distribution line. Phase angle can be used to control the opening of the circuit breaker relative to the reference signal provided by the potential transformer.
Tuca, Maria; Greditzer, Harry Gus; Gausden, Elizabeth Bishop; Uppstrom, Tyler J.; Potter, Hollis G.; Cordasco, Frank A.; Green, Daniel W.
2017-01-01
. Perigraft scarring tended to reduce with follow-up (p=0.057) though not significantly, while synovitis had a significant reduction over time (p=0.01). On average, normalized SI showed no significant differences between measurements taken in different regions of the graft (p=0.58). When comparing the graft SI from 1st to 2nd MRI, no significant differences were found in any of the locations: femoral tunnel (p=0.14), proximal turn (p=0.11), midsubstance (p=0,29), intra-articular distal (p=0.10), or tibial tunnel (p=0.15). All 16 athletes returned to their prior sport at the same level of performance without re-injury. Conclusion: ACL grafts in skeletally immature patients with all-epiphyseal reconstructions maintain a stable intensity signaling at long term MRI follow-up, with no significant signal reduction over time. Despite the sharp turn created at the distal femoral socket aperture in physeal-sparing reconstructions, no particular anatomic location of the graft presents significantly different signal intensity over others. This is the first sequential mri study in pediatric epiphyseal acl reconstructions demonstrating postoperative maintenance of graft integrity and graft signal.
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
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)
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
One of the many visiting theoreticians, R P Feynman, who gave lectures at CERN during the year
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.
Framework for sequential approximate optimization
Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.
2004-01-01
An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python
Sequential and simultaneous choices: testing the diet selection and sequential choice models.
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.
Sequentially pulsed traveling wave accelerator
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.
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.)
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)
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
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.
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)
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.
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.)
Assets and liabilities are the momentum of particles and antiparticles displayed in Feynman-graphs
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.
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.)
Salecker-Wigner-Peres clock, Feynman paths, and a tunneling time that should not exist
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.
A Bayesian Theory of Sequential Causal Learning and Abstract Transfer.
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
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
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...
Sequential logic analysis and synthesis
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
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.
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
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)
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.
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
Evaluation Using Sequential Trials Methods.
Cohen, Mark E.; Ralls, Stephen A.
1986-01-01
Although dental school faculty as well as practitioners are interested in evaluating products and procedures used in clinical practice, research design and statistical analysis can sometimes pose problems. Sequential trials methods provide an analytical structure that is both easy to use and statistically valid. (Author/MLW)
Attack Trees with Sequential Conjunction
Jhawar, Ravi; Kordy, Barbara; Mauw, Sjouke; Radomirović, Sasa; Trujillo-Rasua, Rolando
2015-01-01
We provide the first formal foundation of SAND attack trees which are a popular extension of the well-known attack trees. The SAND at- tack tree formalism increases the expressivity of attack trees by intro- ducing the sequential conjunctive operator SAND. This operator enables the modeling of
The charged Higgs boson mass of the MSSM in the Feynman-diagrammatic approach
Energy Technology Data Exchange (ETDEWEB)
Frank, M. [Karlsruhe Univ. (Germany). Inst. fuer Theoretische Physik; Galeta, L.; Heinemeyer, S. [Instituto de Fisica de Cantabria (CSIC-UC), Santander (Spain); Hahn, T.; Hollik, W. [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Rzehak, H. [CERN, Geneva (Switzerland); Weiglein, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-06-15
The interpretation of the Higgs signal at {proportional_to}126 GeV within the Minimal Supersymmetric Standard Model (MSSM) depends crucially on the predicted properties of the other Higgs states of the model, as the mass of the charged Higgs boson, M{sub H}{sup {sub {+-}}}. This mass is calculated in the Feynman-diagrammatic approach within the MSSM with real parameters. The result includes the complete one-loop contributions and the two-loop contributions of O({alpha}{sub t}{alpha}{sub s}). The one-loop contributions lead to sizable shifts in the M{sub H}{sup {sub {+-}}} prediction, reaching up to {proportional_to}8 GeV for relatively small values of M{sub A}. Even larger effects can occur depending on the sign and size of the {mu} parameter that enters the corrections affecting the relation between the bottom-quark mass and the bottom Yukawa coupling. The two-loop O({alpha}{sub t}{alpha}{sub s}) terms can shift M{sub H}{sup {sub {+-}}} by more than 2 GeV. The two-loop contributions amount to typically about 30% of the one-loop corrections for the examples that we have studied. These effects can be relevant for precision analyses of the charged MSSM Higgs boson.
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.
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
Potential theory, path integrals and the Laplacian of the indicator
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
Differential equations for loop integrals in Baikov representation
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.
Multi-agent sequential hypothesis testing
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
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.
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.)
Robustness of the Sequential Lineup Advantage
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…
Sequential Probability Ration Tests : Conservative and Robust
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
Random sequential adsorption of cubes
Cieśla, Michał; Kubala, Piotr
2018-01-01
Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.
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
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.
DEFF Research Database (Denmark)
Emerek, Ruth
2004-01-01
Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration......Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration...
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.
Projection operator and propagator for an arbitrary integral spin
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
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)
Gómez Rodríguez, Rafael Ángel
2014-01-01
To say that someone possesses integrity is to claim that that person is almost predictable about responses to specific situations, that he or she can prudentially judge and to act correctly. There is a closed interrelationship between integrity and autonomy, and the autonomy rests on the deeper moral claim of all humans to integrity of the person. Integrity has two senses of significance for medical ethic: one sense refers to the integrity of the person in the bodily, psychosocial and intellectual elements; and in the second sense, the integrity is the virtue. Another facet of integrity of the person is la integrity of values we cherish and espouse. The physician must be a person of integrity if the integrity of the patient is to be safeguarded. The autonomy has reduced the violations in the past, but the character and virtues of the physician are the ultimate safeguard of autonomy of patient. A field very important in medicine is the scientific research. It is the character of the investigator that determines the moral quality of research. The problem arises when legitimate self-interests are replaced by selfish, particularly when human subjects are involved. The final safeguard of moral quality of research is the character and conscience of the investigator. Teaching must be relevant in the scientific field, but the most effective way to teach virtue ethics is through the example of the a respected scientist.
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
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)
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.)
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.)
Sequential series for nuclear reactions
International Nuclear Information System (INIS)
Izumo, Ko
1975-01-01
A new time-dependent treatment of nuclear reactions is given, in which the wave function of compound nucleus is expanded by a sequential series of the reaction processes. The wave functions of the sequential series form another complete set of compound nucleus at the limit Δt→0. It is pointed out that the wave function is characterized by the quantities: the number of degrees of freedom of motion n, the period of the motion (Poincare cycle) tsub(n), the delay time t sub(nμ) and the relaxation time tausub(n) to the equilibrium of compound nucleus, instead of the usual quantum number lambda, the energy eigenvalue Esub(lambda) and the total width GAMMAsub(lambda) of resonance levels, respectively. The transition matrix elements and the yields of nuclear reactions also become the functions of time given by the Fourier transform of the usual ones. The Poincare cycles of compound nuclei are compared with the observed correlations among resonance levels, which are about 10 -17 --10 -16 sec for medium and heavy nuclei and about 10 -20 sec for the intermediate resonances. (auth.)
Exploring the sequential lineup advantage using WITNESS.
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.
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)
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)
Sequential lineup presentation: Patterns and policy
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...
The Bacterial Sequential Markov Coalescent.
De Maio, Nicola; Wilson, Daniel J
2017-05-01
Bacteria can exchange and acquire new genetic material from other organisms directly and via the environment. This process, known as bacterial recombination, has a strong impact on the evolution of bacteria, for example, leading to the spread of antibiotic resistance across clades and species, and to the avoidance of clonal interference. Recombination hinders phylogenetic and transmission inference because it creates patterns of substitutions (homoplasies) inconsistent with the hypothesis of a single evolutionary tree. Bacterial recombination is typically modeled as statistically akin to gene conversion in eukaryotes, i.e. , using the coalescent with gene conversion (CGC). However, this model can be very computationally demanding as it needs to account for the correlations of evolutionary histories of even distant loci. So, with the increasing popularity of whole genome sequencing, the need has emerged for a faster approach to model and simulate bacterial genome evolution. We present a new model that approximates the coalescent with gene conversion: the bacterial sequential Markov coalescent (BSMC). Our approach is based on a similar idea to the sequential Markov coalescent (SMC)-an approximation of the coalescent with crossover recombination. However, bacterial recombination poses hurdles to a sequential Markov approximation, as it leads to strong correlations and linkage disequilibrium across very distant sites in the genome. Our BSMC overcomes these difficulties, and shows a considerable reduction in computational demand compared to the exact CGC, and very similar patterns in simulated data. We implemented our BSMC model within new simulation software FastSimBac. In addition to the decreased computational demand compared to previous bacterial genome evolution simulators, FastSimBac provides more general options for evolutionary scenarios, allowing population structure with migration, speciation, population size changes, and recombination hotspots. FastSimBac is
Biased lineups: sequential presentation reduces the problem.
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.
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.
Immediate Sequential Bilateral Cataract Surgery
DEFF Research Database (Denmark)
Kessel, Line; Andresen, Jens; Erngaard, Ditte
2015-01-01
The aim of the present systematic review was to examine the benefits and harms associated with immediate sequential bilateral cataract surgery (ISBCS) with specific emphasis on the rate of complications, postoperative anisometropia, and subjective visual function in order to formulate evidence......-based national Danish guidelines for cataract surgery. A systematic literature review in PubMed, Embase, and Cochrane central databases identified three randomized controlled trials that compared outcome in patients randomized to ISBCS or bilateral cataract surgery on two different dates. Meta-analyses were...... performed using the Cochrane Review Manager software. The quality of the evidence was assessed using the GRADE method (Grading of Recommendation, Assessment, Development, and Evaluation). We did not find any difference in the risk of complications or visual outcome in patients randomized to ISBCS or surgery...
Random and cooperative sequential adsorption
Evans, J. W.
1993-10-01
Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.
International Nuclear Information System (INIS)
Groote, S.; Koerner, J.G.; Pivovarov, A.A.
2007-01-01
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D 0 for different values of dimensions including the most important practical cases D 0 = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added
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…
Trial Sequential Methods for Meta-Analysis
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…
JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
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
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
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
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...
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.
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
Sequential lineup laps and eyewitness accuracy.
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.
Multi-agent sequential hypothesis testing
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.
Sequential Product of Quantum Effects: An Overview
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.
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.
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...
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
Social Influences in Sequential Decision Making.
Directory of Open Access Journals (Sweden)
Markus Schöbel
Full Text Available People often make decisions in a social environment. The present work examines social influence on people's decisions in a sequential decision-making situation. In the first experimental study, we implemented an information cascade paradigm, illustrating that people infer information from decisions of others and use this information to make their own decisions. We followed a cognitive modeling approach to elicit the weight people give to social as compared to private individual information. The proposed social influence model shows that participants overweight their own private information relative to social information, contrary to the normative Bayesian account. In our second study, we embedded the abstract decision problem of Study 1 in a medical decision-making problem. We examined whether in a medical situation people also take others' authority into account in addition to the information that their decisions convey. The social influence model illustrates that people weight social information differentially according to the authority of other decision makers. The influence of authority was strongest when an authority's decision contrasted with private information. Both studies illustrate how the social environment provides sources of information that people integrate differently for their decisions.
Social Influences in Sequential Decision Making
Schöbel, Markus; Rieskamp, Jörg; Huber, Rafael
2016-01-01
People often make decisions in a social environment. The present work examines social influence on people’s decisions in a sequential decision-making situation. In the first experimental study, we implemented an information cascade paradigm, illustrating that people infer information from decisions of others and use this information to make their own decisions. We followed a cognitive modeling approach to elicit the weight people give to social as compared to private individual information. The proposed social influence model shows that participants overweight their own private information relative to social information, contrary to the normative Bayesian account. In our second study, we embedded the abstract decision problem of Study 1 in a medical decision-making problem. We examined whether in a medical situation people also take others’ authority into account in addition to the information that their decisions convey. The social influence model illustrates that people weight social information differentially according to the authority of other decision makers. The influence of authority was strongest when an authority's decision contrasted with private information. Both studies illustrate how the social environment provides sources of information that people integrate differently for their decisions. PMID:26784448
Social Influences in Sequential Decision Making.
Schöbel, Markus; Rieskamp, Jörg; Huber, Rafael
2016-01-01
People often make decisions in a social environment. The present work examines social influence on people's decisions in a sequential decision-making situation. In the first experimental study, we implemented an information cascade paradigm, illustrating that people infer information from decisions of others and use this information to make their own decisions. We followed a cognitive modeling approach to elicit the weight people give to social as compared to private individual information. The proposed social influence model shows that participants overweight their own private information relative to social information, contrary to the normative Bayesian account. In our second study, we embedded the abstract decision problem of Study 1 in a medical decision-making problem. We examined whether in a medical situation people also take others' authority into account in addition to the information that their decisions convey. The social influence model illustrates that people weight social information differentially according to the authority of other decision makers. The influence of authority was strongest when an authority's decision contrasted with private information. Both studies illustrate how the social environment provides sources of information that people integrate differently for their decisions.
Efficient sequential and parallel algorithms for record linkage.
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.
Multilevel sequential Monte Carlo samplers
Beskos, Alexandros; Jasra, Ajay; Law, Kody; Tempone, Raul; Zhou, Yan
2016-01-01
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods which depend on the step-size level . hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretization levels . âˆž>h0>h1â‹¯>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence and a sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. That is, relative to exact sampling and Monte Carlo for the distribution at the finest level . hL. The approach is numerically illustrated on a Bayesian inverse problem. Â© 2016 Elsevier B.V.
Multilevel sequential Monte Carlo samplers
Beskos, Alexandros
2016-08-29
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods which depend on the step-size level . hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretization levels . âˆž>h0>h1â‹¯>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence and a sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. That is, relative to exact sampling and Monte Carlo for the distribution at the finest level . hL. The approach is numerically illustrated on a Bayesian inverse problem. Â© 2016 Elsevier B.V.
Sequential Scintigraphy in Renal Transplantation
Energy Technology Data Exchange (ETDEWEB)
Winkel, K. zum; Harbst, H.; Schenck, P.; Franz, H. E.; Ritz, E.; Roehl, L.; Ziegler, M.; Ammann, W.; Maier-Borst, W. [Institut Fuer Nuklearmedizin, Deutsches Krebsforschungszentrum, Heidelberg, Federal Republic of Germany (Germany)
1969-05-15
Based on experience gained from more than 1600 patients with proved or suspected kidney diseases and on results on extended studies with dogs, sequential scintigraphy was performed after renal transplantation in dogs. After intravenous injection of 500 {mu}Ci. {sup 131}I-Hippuran scintiphotos were taken during the first minute with an exposure time of 15 sec each and thereafter with an exposure of 2 min up to at least 16 min.. Several examinations were evaluated digitally. 26 examinations were performed on 11 dogs with homotransplanted kidneys. Immediately after transplantation the renal function was almost normal arid the bladder was filled in due time. At the beginning of rejection the initial uptake of radioactive Hippuran was reduced. The intrarenal transport became delayed; probably the renal extraction rate decreased. Corresponding to the development of an oedema in the transplant the uptake area increased in size. In cases of thrombosis of the main artery there was no evidence of any uptake of radioactivity in the transplant. Similar results were obtained in 41 examinations on 15 persons. Patients with postoperative anuria due to acute tubular necrosis showed still some uptake of radioactivity contrary to those with thrombosis of the renal artery, where no uptake was found. In cases of rejection the most frequent signs were a reduced initial uptake and a delayed intrarenal transport of radioactive Hippuran. Infarction could be detected by a reduced uptake in distinct areas of the transplant. (author)
Sequential provisional implant prosthodontics therapy.
Zinner, Ira D; Markovits, Stanley; Jansen, Curtis E; Reid, Patrick E; Schnader, Yale E; Shapiro, Herbert J
2012-01-01
The fabrication and long-term use of first- and second-stage provisional implant prostheses is critical to create a favorable prognosis for function and esthetics of a fixed-implant supported prosthesis. The fixed metal and acrylic resin cemented first-stage prosthesis, as reviewed in Part I, is needed for prevention of adjacent and opposing tooth movement, pressure on the implant site as well as protection to avoid micromovement of the freshly placed implant body. The second-stage prosthesis, reviewed in Part II, should be used following implant uncovering and abutment installation. The patient wears this provisional prosthesis until maturation of the bone and healing of soft tissues. The second-stage provisional prosthesis is also a fail-safe mechanism for possible early implant failures and also can be used with late failures and/or for the necessity to repair the definitive prosthesis. In addition, the screw-retained provisional prosthesis is used if and when an implant requires removal or other implants are to be placed as in a sequential approach. The creation and use of both first- and second-stage provisional prostheses involve a restorative dentist, dental technician, surgeon, and patient to work as a team. If the dentist alone cannot do diagnosis and treatment planning, surgery, and laboratory techniques, he or she needs help by employing the expertise of a surgeon and a laboratory technician. This team approach is essential for optimum results.
Energy Technology Data Exchange (ETDEWEB)
Soltz, R. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Danagoulian, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sheets, S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Korbly, S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hartouni, E. P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2013-05-22
Theoretical calculations indicate that the value of the Feynman variance, Y2F for the emitted distribution of neutrons from ssionable exhibits a strong monotonic de- pendence on a the multiplication, M, of a quantity of special nuclear material. In 2012 we performed a series of measurements at the Passport Inc. facility using a 9- MeV bremsstrahlung CW beam of photons incident on small quantities of uranium with liquid scintillator detectors. For the set of objects studies we observed deviations in the expected monotonic dependence, and these deviations were later con rmed by MCNP simulations. In this report, we modify the theory to account for the contri- bution from the initial photo- ssion and benchmark the new theory with a series of MCNP simulations on DU, LEU, and HEU objects spanning a wide range of masses and multiplication values.
Directory of Open Access Journals (Sweden)
Dong Hyun Cho
2017-01-01
Full Text Available Using a simple formula for conditional expectations over continuous paths, we will evaluate conditional expectations which are types of analytic conditional Fourier-Feynman transforms and conditional convolution products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the measures on the Borel class of L2[0,T]. We will then investigate their relationships. Particularly, we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we will establish change of scale formulas for the conditional transforms and the conditional convolution products. In these evaluation formulas and change of scale formulas, we use multivariate normal distributions so that the conditioning function does not contain present positions of the paths.
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.
Homological Perturbation Theory for Nonperturbative Integrals
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.
DEFF Research Database (Denmark)
Olwig, Karen Fog
2011-01-01
, while the countries have adopted disparate policies and ideologies, differences in the actual treatment and attitudes towards immigrants and refugees in everyday life are less clear, due to parallel integration programmes based on strong similarities in the welfare systems and in cultural notions...... of equality in the three societies. Finally, it shows that family relations play a central role in immigrants’ and refugees’ establishment of a new life in the receiving societies, even though the welfare society takes on many of the social and economic functions of the family....
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)
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].
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.
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
Efficacy of premixed versus sequential administration of ...
African Journals Online (AJOL)
sequential administration in separate syringes on block characteristics, haemodynamic parameters, side effect profile and postoperative analgesic requirement. Trial design: This was a prospective, randomised clinical study. Method: Sixty orthopaedic patients scheduled for elective lower limb surgery under spinal ...
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)
Structural Consistency, Consistency, and Sequential Rationality.
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...
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).
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.
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.
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
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
Breaking from binaries - using a sequential mixed methods design.
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.
Frabboni, Stefano; Gazzadi, Gian Carlo; Grillo, Vincenzo; Pozzi, Giulio
2015-07-01
Modern nanotechnology tools allowed us to prepare slits of 90 nm width and 450 nm spacing in a screen almost completely opaque to 200 keV electrons. Then by covering both slits with a layer of amorphous material and carrying out the experiment in a conventional transmission electron microscope equipped with an energy filter we can demonstrate that the diffraction pattern, taken by selecting the elastically scattered electrons, shows the presence of interference fringes, but with a bimodal envelope which can be accounted for by taking into account the non-constant thickness of the deposited layer. However, the intensity of the inelastically scattered electrons in the diffraction plane is very broad and at the limit of detectability. Therefore the experiment was repeated using an aluminum film and a microscope also equipped with a Schottky field emission gun. It was thus possible to observe also the image due to the inelastically scattered electron, which does not show interference phenomena both in the Fraunhofer or Fresnel regimes. If we assume that inelastic scattering through the thin layer covering the slits provides the dissipative process of interaction responsible for the localization mechanism, then these experiments can be considered a variant of the Feynman which-way thought experiment. Copyright © 2015 Elsevier B.V. All rights reserved.
Sequential dependencies in magnitude scaling of loudness
DEFF Research Database (Denmark)
Joshi, Suyash Narendra; Jesteadt, Walt
2013-01-01
Ten normally hearing listeners used a programmable sone-potentiometer knob to adjust the level of a 1000-Hz sinusoid to match the loudness of numbers presented to them in a magnitude production task. Three different power-law exponents (0.15, 0.30, and 0.60) and a log-law with equal steps in d......B were used to program the sone-potentiometer. The knob settings systematically influenced the form of the loudness function. Time series analysis was used to assess the sequential dependencies in the data, which increased with increasing exponent and were greatest for the log-law. It would be possible......, therefore, to choose knob properties that minimized these dependencies. When the sequential dependencies were removed from the data, the slope of the loudness functions did not change, but the variability decreased. Sequential dependencies were only present when the level of the tone on the previous trial...
MPL-A program for computations with iterated integrals on moduli spaces of curves of genus zero
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.
Integrated and sequential anaerobic/aerobic biodegradation of azo dyes
Tan, N.G.C.
2001-01-01
Azo dyes constitute a major class of environmental pollutants accounting for 60 to 70% of all dyes and pigments used. These compounds are characterized by aromatic moieties linked together with azo groups (-N=N-). The release of azo dyes into the environment is a concern due to coloration
Dihydroazulene photoswitch operating in sequential tunneling regime
DEFF Research Database (Denmark)
Broman, Søren Lindbæk; Lara-Avila, Samuel; Thisted, Christine Lindbjerg
2012-01-01
to electrodes so that the electron transport goes by sequential tunneling. To assure weak coupling, the DHA switching kernel is modified by incorporating p-MeSC6H4 end-groups. Molecules are prepared by Suzuki cross-couplings on suitable halogenated derivatives of DHA. The synthesis presents an expansion of our......, incorporating a p-MeSC6H4 anchoring group in one end, has been placed in a silver nanogap. Conductance measurements justify that transport through both DHA (high resistivity) and VHF (low resistivity) forms goes by sequential tunneling. The switching is fairly reversible and reenterable; after more than 20 ON...
Asynchronous Operators of Sequential Logic Venjunction & Sequention
Vasyukevich, Vadim
2011-01-01
This book is dedicated to new mathematical instruments assigned for logical modeling of the memory of digital devices. The case in point is logic-dynamical operation named venjunction and venjunctive function as well as sequention and sequentional function. Venjunction and sequention operate within the framework of sequential logic. In a form of the corresponding equations, they organically fit analytical expressions of Boolean algebra. Thus, a sort of symbiosis is formed using elements of asynchronous sequential logic on the one hand and combinational logic on the other hand. So, asynchronous
Interpretability degrees of finitely axiomatized sequential theories
Visser, Albert
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory-like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB-have suprema. This partially answers a question posed
Interpretability Degrees of Finitely Axiomatized Sequential Theories
Visser, Albert
2012-01-01
In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory —like Elementary Arithmetic EA, IΣ1, or the Gödel-Bernays theory of sets and classes GB— have suprema. This partially answers a question
S.M.P. SEQUENTIAL MATHEMATICS PROGRAM.
CICIARELLI, V; LEONARD, JOSEPH
A SEQUENTIAL MATHEMATICS PROGRAM BEGINNING WITH THE BASIC FUNDAMENTALS ON THE FOURTH GRADE LEVEL IS PRESENTED. INCLUDED ARE AN UNDERSTANDING OF OUR NUMBER SYSTEM, AND THE BASIC OPERATIONS OF WORKING WITH WHOLE NUMBERS--ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION. COMMON FRACTIONS ARE TAUGHT IN THE FIFTH, SIXTH, AND SEVENTH GRADES. A…
Sequential and Simultaneous Logit: A Nested Model.
van Ophem, J.C.M.; Schram, A.J.H.C.
1997-01-01
A nested model is presented which has both the sequential and the multinomial logit model as special cases. This model provides a simple test to investigate the validity of these specifications. Some theoretical properties of the model are discussed. In the analysis a distribution function is
Sensitivity Analysis in Sequential Decision Models.
Chen, Qiushi; Ayer, Turgay; Chhatwal, Jagpreet
2017-02-01
Sequential decision problems are frequently encountered in medical decision making, which are commonly solved using Markov decision processes (MDPs). Modeling guidelines recommend conducting sensitivity analyses in decision-analytic models to assess the robustness of the model results against the uncertainty in model parameters. However, standard methods of conducting sensitivity analyses cannot be directly applied to sequential decision problems because this would require evaluating all possible decision sequences, typically in the order of trillions, which is not practically feasible. As a result, most MDP-based modeling studies do not examine confidence in their recommended policies. In this study, we provide an approach to estimate uncertainty and confidence in the results of sequential decision models. First, we provide a probabilistic univariate method to identify the most sensitive parameters in MDPs. Second, we present a probabilistic multivariate approach to estimate the overall confidence in the recommended optimal policy considering joint uncertainty in the model parameters. We provide a graphical representation, which we call a policy acceptability curve, to summarize the confidence in the optimal policy by incorporating stakeholders' willingness to accept the base case policy. For a cost-effectiveness analysis, we provide an approach to construct a cost-effectiveness acceptability frontier, which shows the most cost-effective policy as well as the confidence in that for a given willingness to pay threshold. We demonstrate our approach using a simple MDP case study. We developed a method to conduct sensitivity analysis in sequential decision models, which could increase the credibility of these models among stakeholders.
Sequential models for coarsening and missingness
Gill, R.D.; Robins, J.M.
1997-01-01
In a companion paper we described what intuitively would seem to be the most general possible way to generate Coarsening at Random mechanisms a sequential procedure called randomized monotone coarsening Counterexamples showed that CAR mechanisms exist which cannot be represented in this way Here we
Sequential motor skill: cognition, perception and action
Ruitenberg, M.F.L.
2013-01-01
Discrete movement sequences are assumed to be the building blocks of more complex sequential actions that are present in our everyday behavior. The studies presented in this dissertation address the (neuro)cognitive underpinnings of such movement sequences, in particular in relationship to the role
Sequential decoders for large MIMO systems
Ali, Konpal S.; Abediseid, Walid; Alouini, Mohamed-Slim
2014-01-01
the Sequential Decoder using the Fano Algorithm for large MIMO systems. A parameter called the bias is varied to attain different performance-complexity trade-offs. Low values of the bias result in excellent performance but at the expense of high complexity
A framework for sequential multiblock component methods
Smilde, A.K.; Westerhuis, J.A.; Jong, S.de
2003-01-01
Multiblock or multiset methods are starting to be used in chemistry and biology to study complex data sets. In chemometrics, sequential multiblock methods are popular; that is, methods that calculate one component at a time and use deflation for finding the next component. In this paper a framework
Classical and sequential limit analysis revisited
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.
Sequential spatial processes for image analysis
M.N.M. van Lieshout (Marie-Colette); V. Capasso
2009-01-01
htmlabstractWe give a brief introduction to sequential spatial processes. We discuss their definition, formulate a Markov property, and indicate why such processes are natural tools in tackling high level vision problems. We focus on the problem of tracking a variable number of moving objects
Sequential spatial processes for image analysis
Lieshout, van M.N.M.; Capasso, V.
2009-01-01
We give a brief introduction to sequential spatial processes. We discuss their definition, formulate a Markov property, and indicate why such processes are natural tools in tackling high level vision problems. We focus on the problem of tracking a variable number of moving objects through a video
Sequential Analysis: Hypothesis Testing and Changepoint Detection
2014-07-11
maintains the flexibility of deciding sooner than the fixed sample size procedure at the price of some lower power [13, 514]. The sequential probability... markets , detection of signals with unknown arrival time in seismology, navigation, radar and sonar signal processing, speech segmentation, and the... skimming cruise missile can yield a significant increase in the probability of raid annihilation. Furthermore, usually detection systems are
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
Truly costly sequential search and oligopolistic pricing
Janssen, Maarten C W; Moraga-González, José Luis; Wildenbeest, Matthijs R.
We modify the paper of Stahl (1989) [Stahl, D.O., 1989. Oligopolistic pricing with sequential consumer search. American Economic Review 79, 700-12] by relaxing the assumption that consumers obtain the first price quotation for free. When all price quotations are costly to obtain, the unique
Zips : mining compressing sequential patterns in streams
Hoang, T.L.; Calders, T.G.K.; Yang, J.; Mörchen, F.; Fradkin, D.; Chau, D.H.; Vreeken, J.; Leeuwen, van M.; Faloutsos, C.
2013-01-01
We propose a streaming algorithm, based on the minimal description length (MDL) principle, for extracting non-redundant sequential patterns. For static databases, the MDL-based approach that selects patterns based on their capacity to compress data rather than their frequency, was shown to be
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.
Adult Word Recognition and Visual Sequential Memory
Holmes, V. M.
2012-01-01
Two experiments were conducted investigating the role of visual sequential memory skill in the word recognition efficiency of undergraduate university students. Word recognition was assessed in a lexical decision task using regularly and strangely spelt words, and nonwords that were either standard orthographically legal strings or items made from…
Terminating Sequential Delphi Survey Data Collection
Kalaian, Sema A.; Kasim, Rafa M.
2012-01-01
The Delphi survey technique is an iterative mail or electronic (e-mail or web-based) survey method used to obtain agreement or consensus among a group of experts in a specific field on a particular issue through a well-designed and systematic multiple sequential rounds of survey administrations. Each of the multiple rounds of the Delphi survey…
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
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.
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
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
Online Sequential Projection Vector Machine with Adaptive Data Mean Update.
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.
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.
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.
Heuristic and optimal policy computations in the human brain during sequential decision-making.
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.
Covariant path integrals on hyperbolic surfaces
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).
A fast and accurate online sequential learning algorithm for feedforward networks.
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.
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.
Impact of Diagrams on Recalling Sequential Elements in Expository Texts.
Guri-Rozenblit, Sarah
1988-01-01
Examines the instructional effectiveness of abstract diagrams on recall of sequential relations in social science textbooks. Concludes that diagrams assist significantly the recall of sequential relations in a text and decrease significantly the rate of order mistakes. (RS)
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
Energy Technology Data Exchange (ETDEWEB)
Racz, A.; Lux, I. [Hungarian Academy of Sciences, Budapest (Hungary). Atomic Energy Research Inst.
1996-04-16
The applicability of the classical sequential probability ratio testing (SPRT) for early failure detection problems is limited by the fact that there is an extra time delay between the occurrence of the failure and its first recognition. Chien and Adams developed a method to minimize this time for the case when the problem can be formulated as testing the mean value of a Gaussian signal. In our paper we propose a procedure that can be applied for both mean and variance testing and that minimizes the time delay. The method is based on a special parametrization of the classical SPRT. The one-sided sequential tests (OSST) can reproduce the results of the Chien-Adams test when applied for mean values. (author).
Documentscape: Intertextuality, Sequentiality & Autonomy at Work
DEFF Research Database (Denmark)
Christensen, Lars Rune; Bjørn, Pernille
2014-01-01
On the basis of an ethnographic field study, this article introduces the concept of documentscape to the analysis of document-centric work practices. The concept of documentscape refers to the entire ensemble of documents in their mutual intertextual interlocking. Providing empirical data from...... a global software development case, we show how hierarchical structures and sequentiality across the interlocked documents are critical to how actors make sense of the work of others and what to do next in a geographically distributed setting. Furthermore, we found that while each document is created...... as part of a quasi-sequential order, this characteristic does not make the document, as a single entity, into a stable object. Instead, we found that the documents were malleable and dynamic while suspended in intertextual structures. Our concept of documentscape points to how the hierarchical structure...
Sequential Service Restoration for Unbalanced Distribution Systems and Microgrids
International Nuclear Information System (INIS)
Chen, Bo; Chen, Chen; Wang, Jianhui; Butler-Purry, Karen L.
2017-01-01
The resilience and reliability of modern power systems are threatened by increasingly severe weather events and cyber-physical security events. An effective restoration methodology is desired to optimally integrate emerging smart grid technologies and pave the way for developing self-healing smart grids. In this paper, a sequential service restoration (SSR) framework is proposed to generate restoration solutions for distribution systems and microgrids in the event of large-scale power outages. The restoration solution contains a sequence of control actions that properly coordinate switches, distributed generators, and switchable loads to form multiple isolated microgrids. The SSR can be applied for three-phase unbalanced distribution systems and microgrids and can adapt to various operation conditions. Mathematical models are introduced for three-phase unbalanced power flow, voltage regulators, transformers, and loads. Furthermore, the SSR problem is formulated as a mixed-integer linear programming model, and its effectiveness is evaluated via the modified IEEE 123 node test feeder.
On the effect of response transformations in sequential parameter optimization.
Wagner, Tobias; Wessing, Simon
2012-01-01
Parameter tuning of evolutionary algorithms (EAs) is attracting more and more interest. In particular, the sequential parameter optimization (SPO) framework for the model-assisted tuning of stochastic optimizers has resulted in established parameter tuning algorithms. In this paper, we enhance the SPO framework by introducing transformation steps before the response aggregation and before the actual modeling. Based on design-of-experiments techniques, we empirically analyze the effect of integrating different transformations. We show that in particular, a rank transformation of the responses provides significant improvements. A deeper analysis of the resulting models and additional experiments with adaptive procedures indicates that the rank and the Box-Cox transformation are able to improve the properties of the resultant distributions with respect to symmetry and normality of the residuals. Moreover, model-based effect plots document a higher discriminatory power obtained by the rank transformation.
Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment
Carpenter, James R.; Markley, F Landis
2014-01-01
This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.
A minimax procedure in the context of sequential mastery testing
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
Applying the minimax principle to sequential mastery testing
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
Optimal Sequential Rules for Computer-Based Instruction.
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…
On Locally Most Powerful Sequential Rank Tests
Czech Academy of Sciences Publication Activity Database
Kalina, Jan
2017-01-01
Roč. 36, č. 1 (2017), s. 111-125 ISSN 0747-4946 R&D Projects: GA ČR GA17-07384S Grant - others:Nadační fond na podporu vědy(CZ) Neuron Institutional support: RVO:67985807 Keywords : nonparametric test s * sequential ranks * stopping variable Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.339, year: 2016
Sequential pattern recognition by maximum conditional informativity
Czech Academy of Sciences Publication Activity Database
Grim, Jiří
2014-01-01
Roč. 45, č. 1 (2014), s. 39-45 ISSN 0167-8655 R&D Projects: GA ČR(CZ) GA14-02652S; GA ČR(CZ) GA14-10911S Keywords : Multivariate statistics * Statistical pattern recognition * Sequential decision making * Product mixtures * EM algorithm * Shannon information Subject RIV: IN - Informatics, Computer Sci ence Impact factor: 1.551, year: 2014 http://library.utia.cas.cz/separaty/2014/RO/grim-0428565.pdf
Comparing two Poisson populations sequentially: an application
International Nuclear Information System (INIS)
Halteman, E.J.
1986-01-01
Rocky Flats Plant in Golden, Colorado monitors each of its employees for radiation exposure. Excess exposure is detected by comparing the means of two Poisson populations. A sequential probability ratio test (SPRT) is proposed as a replacement for the fixed sample normal approximation test. A uniformly most efficient SPRT exists, however logistics suggest using a truncated SPRT. The truncated SPRT is evaluated in detail and shown to possess large potential savings in average time spent by employees in the monitoring process