Comment on generalized Euler--Pochhammer integral representation for single-loop Feynman amplitudes
International Nuclear Information System (INIS)
Mano, K.
1975-01-01
Use of the F/subD/ function of Lauricella is suggested in obtaining the Euler-Pochhammer-type integral representation for the single-loop Feynman amplitude of arbitrary order. It is shown that the F/subD/ function is naturally suited in that it leads to a recurrence relation for the amplitude under consideration
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.
Functional equations for Feynman integrals
International Nuclear Information System (INIS)
Tarasov, O.V.
2011-01-01
New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains
Determine Arbitrary Feynman Integrals by Vacuum Integrals
Liu, Xiao; Ma, Yan-Qing
2018-01-01
By introducing an auxiliary parameter, we find a series representation for Feynman integral, which is defined as analytical continuation of a calculable series. To obtain the series representation, one only needs to deal with some much simpler vacuum integrals. The series representation therefore translates the problem of computing Feynman integrals to the problem of performing analytical continuations. As a Feynman integral is fully determined by its series representation, its reduction rela...
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.
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.
2011-05-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with externalmomenta. This is based on sums over signedminors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently. (orig.)
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
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.)
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
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.
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.
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.
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.)
Complex potentials and rigorous Feynman integrals
International Nuclear Information System (INIS)
Exner, P.
1982-01-01
It is shown that the dynamics of dissipative quantum-mechanical systems described by complex potentials can be expressed by means of the Feynman-type path integrals. For the latter, three rigorous definitions are used: they are essentially those of Albeverio and Hoegh-Krohn, Truman, Nelson and Faris. The potentials considered include those bounded, square-integrable for the configuration-space dimension <= 3, and that corresponding to the damped harmonic oscillator. (author)
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
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 ren...
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.)
Evaluating Feynman integrals by the hypergeometry
Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin
2018-02-01
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.
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
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.
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...
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
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
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.
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
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
A systematization for one-loop 4D Feynman integrals
International Nuclear Information System (INIS)
Battistel, O.A.; Dallabona, G.
2006-01-01
We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered. (orig.)
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.
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...
A quasi-finite basis for multi-loop Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Manteuffel, Andreas von [PRISMA Cluster of Excellence & Institute of PhysicsJohannes Gutenberg University, 55099 Mainz (Germany); Panzer, Erik [Institutes of Physics and Mathematics, Humboldt-Universität zu Berlin,Unter den Linden 6, 10099 Berlin (Germany); Institute des Hautes Études Scientifiques, Le Bois Marie,35 Route de Chartres, 91440 Bures-sur-Yvette (France); Schabinger, Robert M. [PRISMA Cluster of Excellence & Institute of PhysicsJohannes Gutenberg University, 55099 Mainz (Germany)
2015-02-18
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical limitations of the original procedure by employing integration by parts reduction.
Beam spread functions calculated using Feynman path integrals
Kilgo, Paul; Tessendorf, Jerry
2017-07-01
A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread functions (BSFs), a commonly studied experimental property of many types of media. The calculations are compared against measured BSFs of sea ice. Analysis shows differently-shaped BSFs, and suggests the width parameter of the calculated BSF's Gaussian fit approaches a value in the limit of the number of path segments. A projection is attempted, but suggests a larger number of path segments would not increase the width of the calculated BSF. The trial suggests the approach is numerically stable, but requires further testing to ensure scientific accuracy.
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 2 F 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
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Tarasov, Oleg V.
2011-08-01
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 1 . From the comparison of this expression with a previously known one, a new relation between the Appell functions F 1 and F 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 1 function with particular arguments to the hypergeometric function 3 F 2 is derived. By comparing results for a particular one-loop vertex integral obtained using different methods, a new relationship between F 1 functions corresponding to a quadratic transformation of the arguments is established. Another reduction formula for the F 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 1 function and the Gaussian hypergeometric function 2 F 1 whose argument is the ratio of polynomials of degree six is presented. (orig.)
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.)
Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, Johannes; Dubovyk, Ievgen; Ochman, Michal; Raab, Clemens G.; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Gluza, Janusz [Uniwersytet Slaski, Katowice (Poland). Inst. of Physics and Chemistry; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2014-07-15
The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented. The ultimate goal of this project is the automatic evaluation of MB representations for multiloop scalar and tensor Feynman integrals through infinite sums, preferably with analytic solutions. We shortly describe a strategy of further algebraic summation.
arXiv The diagrammatic coaction and the algebraic structure of cut Feynman integrals
Abreu, Samuel; Duhr, Claude; Gardi, Einan
We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The coaction encodes the algebraic structure of these integrals, and offers ways to extract important properties of complicated integrals from simpler functions. In particular, it gives direct access to discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they satisfy, which we illustrate in the case of the pentagon.
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.)
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.
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.)
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.
Calculation of the Feynman integrals by means of the Monte Carlo method
International Nuclear Information System (INIS)
Filinov, V.S.
1986-01-01
The Monte Carlo method (the Metropolis algorithm), which is employed extensively in lattice gauge theories and quantum mechanics, was applicable only to the euclidean version of the Feynman path integrals, i.e. it was valid for evaluating the integrals of real functions. In the present work the Monte Carlo method is extended to the evaluation of the integrals of complex-valued functions. The Feynman path integrals representing the time-dependent Green function of the one-dimensional non-stationary Schroedinger equation have been calculated for the harmonic oscillator and the particle motion in barrier- and well-type potential fields. The numerical results are in reasonable agreement with the analytical estimates, in spite of the presence of singularities in the Green functions. (orig.)
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
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.
One-loop tensor Feynman integral reduction with signed minors
DEFF Research Database (Denmark)
Fleischer, Jochem; Riemann, Tord; Yundin, Valery
2012-01-01
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 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...
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.)
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.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. Richard Feynman. Articles written in Resonance – Journal of Science Education. Volume 16 Issue 9 September 2011 pp 860-873 Reflections. What is Science? Richard Feynman · More Details Fulltext PDF ...
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...
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...
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.
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
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.
Ma, Chao; Ma, Qinghua; Yao, Haixiang; Hou, Tiancheng
2018-03-01
In this paper, we propose to use the Fractional Stable Process (FSP) for option pricing. The FSP is one of the few candidates to directly model a number of desired empirical properties of asset price risk neutral dynamics. However, pricing the vanilla European option under FSP is difficult and problematic. In the paper, built upon the developed Feynman Path Integral inspired techniques, we present a novel computational model for option pricing, i.e. the Fractional Stable Process Path Integral (FSPPI) model under a general fractional stable distribution that tackles this problem. Numerical and empirical experiments show that the proposed pricing model provides a correction of the Black-Scholes pricing error - overpricing long term options, underpricing short term options; overpricing out-of-the-money options, underpricing in-the-money options without any additional structures such as stochastic volatility and a jump process.
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.
Reduction method for dimensionally regulatedone-loop N-point Feynman integrals
Duplančić, G.; Nižić, B.
2004-06-01
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D = 6, a triangle integral in D = 4, and a general two-point integral in D space-time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large-momentum transfer in PQCD. The iterative structure makes it easy to implement the formalism in an algebraic computer program.
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…
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.)
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
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.)
Szabo, Zoltan I.
2006-01-01
The problem of infinities (divergent integrals) appearing in quantum field theory or elementary particle physics are treated by renormalization in the current theories. By this perturbative tool the desired finite quantities are produced by differences of infinities. This paper gives a new non-perturbative approach to this problem. Namely, the Hilbert space on which the quantum Hamilton operator $H$ is acting, is decomposed into subspaces, called Zeeman zones, which are invariant under the ac...
Barnea, A. Ronny; Cheshnovsky, Ori; Even, Uzi
2018-02-01
Interference experiments have been paramount in our understanding of quantum mechanics and are frequently the basis of testing the superposition principle in the framework of quantum theory. In recent years, several studies have challenged the nature of wave-function interference from the perspective of Born's rule—namely, the manifestation of so-called high-order interference terms in a superposition generated by diffraction of the wave functions. Here we present an experimental test of multipath interference in the diffraction of metastable helium atoms, with large-number counting statistics, comparable to photon-based experiments. We use a variation of the original triple-slit experiment and accurate single-event counting techniques to provide a new experimental bound of 2.9 ×10-5 on the statistical deviation from the commonly approximated null third-order interference term in Born's rule for matter waves. Our value is on the order of the maximal contribution predicted for multipath trajectories by Feynman path integrals.
The Errors of Feynman and Hibbs
Indian Academy of Sciences (India)
in physics education. Keywords. Quantum mechanics, path inte- grals, Albert Hibbs, Feynman's errors, mathematical rigor. In 1965, Richard Feynman and his former grad- uate student Albert Hibbs published a textbook on Quantum Mechanics and Path Integrals. This text. { based on Feynman's teaching of graduate-level.
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.
Selected papers of Richard Feynman with commentary
2000-01-01
These scientific papers of Richard Feynman are renowned for their brilliant content and the author's striking original style. They are grouped by topic: path integral approach to the foundations of quantum mechanics and quantum field theory, renormalized quantum electrodynamics, theory of superfluid liquid helium, theory of the Fermi interaction, polarons, gravitation, partons, computer theory, etc. Comments on Feynman's topics are provided by the editor, together with biographical notes and a complete bibliography of Feynman's publications.
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
Dual representation for the generating functional of the Feynman path-integral
Directory of Open Access Journals (Sweden)
Marco Matone
2016-09-01
Full Text Available The generating functional for scalar theories admits a representation which is dual with respect to the one introduced by Schwinger, interchanging the role of the free and interacting terms. It maps ∫V(δJ and JΔJ to δϕcΔδϕc and ∫V(ϕc, respectively, with ϕc=∫JΔ and Δ the Feynman propagator. Comparing the Schwinger representation with its dual version one gets a little known relation that we prove to be a particular case of a more general operatorial relation. We then derive a new representation of the generating functional T[ϕc]=W[J] expressed in terms of covariant derivatives acting on 1 T[ϕc]=NN0exp(−U0[ϕc]exp(−∫V(Dϕc−⋅1 where Dϕ±(x=∓Δδδϕ(x+ϕ(x. The dual representation, which is deeply related to the Hermite polynomials, is the key to express the generating functional associated to a sum of potentials in terms of factorized generating functionals. This is applied to renormalization, leading to a factorization of the counterterms of the interaction. We investigate the structure of the functional generator for normal ordered potentials and derive an infinite set of relations in the case of the potential λn!:ϕn: . Such relations are explicitly derived by using the Faà di Bruno formula. This also yields the explicit expression of the generating functional of connected Green's functions.
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,"
Wong, Kin-Yiu; Xu, Yuqing; Xu, Liang
2015-11-01
Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O
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.
Uniform product formulae with application to the Feynman-Nelson integral for open systems
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.L.
1981-01-01
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
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.)
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. Richard P Feynman. Articles written in Resonance – Journal of Science Education. Volume 2 Issue 12 December 1997 pp 107-107 Classics. The Theory of Positrons · Richard P Feynman · More Details Fulltext PDF. Volume 16 Issue 9 September 2011 pp ...
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.
Jones, Richard
2009-12-01
Irrespective of what he got right and what he got wrong in his famous 1959 lecture, Richard Feynman's vision and imagination have had an important role in the development of nanoscience and nanotechnology, as Richard Jones reports.
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)
store for anyone who dares to follow the beat of a different drum..” – Julian Schwinger. “… the most original mind of his generation.” – Freeman ... conversation with Herbert Jehle in 1941 that led Feynman to a seminal 1933 paper of Dirac in which he had drawn attention to an analogy between the classical action principle, ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 5. Feynman's Lost Lecture - The Motion of the Planets Around the Sun. Shailesh A Shirali. Book Review Volume 3 Issue 5 May 1998 pp 78-80. Fulltext. Click here to view fulltext PDF. Permanent link:
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
Gordon, Lyndsay G. M.
2011-12-01
Feynman1 argued that a ratchet of the type used in heavy machinery could be used, in a scaled-down version, to show that the second law of thermodynamics is not just a statistical law, but has absolute status. Hidden is the assumption that this model represented the completely general example of this device—and that it remained so, across the complete range of magnitudes from macro- to micro-domains. It will be argued here, that Feynman's example is only one construct of a ratchet and cannot represent the general case. A mechanism, with sufficient difference and confined to the micro-domain, is the subject of the present discussion. Its unique feature is the compressible nature of the pawl as it librates in pawl-space. The motions of the gear and the pawl are governed by the energy exchanges between them and with the ambient gas. The average linear pressure on the pawl which varies with the magnitude of pawl-space is associated with the compressibility of the pawl. Feynman's objective was to show that the prototypal ratchet is incapable of converting heat into work in a manner contrary to the second law. The dubious nature of his examination is not due to an incorrect analysis of his thought experiment, but lies within the assumption that his example represented the general case. In contrast, the ratchet analyzed here does not conform to the principle of detailed balance and thereby the absolute status of the law remains an open question.
International Nuclear Information System (INIS)
Milgram, M.S.; Lee, H.C.
1987-03-01
A comprehensive set of two-point tensor integrals with up to 3 Lorentz indices for Yang-Mills theories in the light-cone gauge defined in the Mandelstam-Leibbrandt prescription is evaluated and presented in tabulated form
Energy Technology Data Exchange (ETDEWEB)
Tanizaki, Yuya, E-mail: yuya.tanizaki@riken.jp [Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan); Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198 (Japan); Koike, Takayuki, E-mail: tkoike@ms.u-tokyo.ac.jp [Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914 (Japan)
2014-12-15
Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.
Stability Analysis and Controller Synthesis for Digital Single-Loop Voltage-Controlled Inverters
DEFF Research Database (Denmark)
Wang, Xiongfei; Loh, Poh Chiang; Blaabjerg, Frede
2016-01-01
This paper analyzes first the stability of single-loop digital voltage control scheme for the LC-filtered voltage source inverters. It turns out that the phase lag, caused by the time delay of digital control system and by the use of integral controller, can stabilize the voltage loop without...... damping of LC-filter resonance. The stability regions are then identified with alternative voltage controller synthesized. For further widening the stability region, an active damping approach is proposed and co-designed with the voltage controller in the discrete z-domain. Simulations and experimental...
Goodstein, David L.
1989-01-01
The February issue of PHYSICS TODAY celebrated the life of Richard Feynman. It seems to me appropriate to make some mention of Feynman's opinion of PHYSICS TODAY. I believe that what follows can count as the formal publication of a historically important document.
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
Effect of the shape on the spin state and exchange in quantum dots. Feynman path integral analysis
International Nuclear Information System (INIS)
Shevkunov, S. V.
2015-01-01
The ab initio computer simulation of the mixed quantum states of 1–5-nm model ellipsoid quantum dots with “soft” walls containing two and three quantum-indistinguishable nonrelativistic electrons has been performed by the path integral method. The calculation has been carried out beyond the single-electron and mean-field approximations with the fundamentally exact inclusion of Coulomb and exchange correlations of all orders and the spin variable. Distributions over the eigenfunctions of the spin-squared operator, as well as the equilibrium spin numbers, have been obtained depending on the shape of a quantum dot and the temperature. The complete set of basis functions symmetrized in permutations according to the spin of the system has been obtained by application of the Young symmetry operators. The dependence of the energy on the shape of the quantum dot corresponds to the negative sign of the surface tension at its boundary. The calculation indicates that the spin magnetic susceptibility in the system of two electrons decreases strongly for spherical quantum dots (“pairing” of spins) and the temperature dependences have a pronounced maximum whose position depends on the shape of the quantum dot. For three electrons in an oblate quantum dot, the inversion of the energy levels of spin states is observed and affects the spin magnetic susceptibility. The results indicate a strong dependence of the energy of collective spin states of electrons on the detailed inclusion of exchange and Coulomb spatial correlations
Functional analysis and the Feynman operator calculus
Gill, Tepper L
2016-01-01
This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.
Quality Scalability Compression on Single-Loop Solution in HEVC
Directory of Open Access Journals (Sweden)
Mengmeng Zhang
2014-01-01
Full Text Available This paper proposes a quality scalable extension design for the upcoming high efficiency video coding (HEVC standard. In the proposed design, the single-loop decoder solution is extended into the proposed scalable scenario. A novel interlayer intra/interprediction is added to reduce the amount of bits representation by exploiting the correlation between coding layers. The experimental results indicate that the average Bjøntegaard delta rate decrease of 20.50% can be gained compared with the simulcast encoding. The proposed technique achieved 47.98% Bjøntegaard delta rate reduction compared with the scalable video coding extension of the H.264/AVC. Consequently, significant rate savings confirm that the proposed method achieves better performance.
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
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.
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
Differential equations for Feynman graph amplitudes
International Nuclear Information System (INIS)
Remiddi, E.
1997-01-01
It is by now well established that, by means of the integration by part identities all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is shown in this paper that the integration by part identities can be further used for obtaining a linear system of first-order differential equations for the master integrals themselves. The equations con then be used for the numerical evaluation of the amplitudes as well as for investigating their analytic properties, such as the asymptotic and threshold behaviours and the corresponding expansions (and for analytic integration purposes, when possible). The new method is illustrated through its somewhat detailed application to the case of the one-loop self-mass amplitude, by explicitly working out expansions and quadrature formulas, both in arbitrary continuous dimension n and in the n→4 limit. It is then shortly discussed which features of the new method are expected to work in the more general case of multi-point, multi-loop amplitudes
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)
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.)
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
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.)
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 ...
DEFF Research Database (Denmark)
Pan, Donghua; Ruan, Xinbo; Wang, Xiongfei
2018-01-01
Single-loop current control is an attractive scheme for the LCL-type grid-connected inverter due to its simplicity and low cost. However, conventional single-loop control schemes, which command either the inverter current or the grid current, are subject to the specific resonance frequency region...
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.
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
Single-loop renormalizations and properties of radiative corrections in the Fried-Yennie gauge
International Nuclear Information System (INIS)
Karshenboim, S.G.; Shelyuto, V.A.; Eides, M.I.
1988-01-01
Single-loop radiative corrections are studied in the Fried-Yennie gauge. It is shown that in this gauge the usual subtraction procedure on the mass shell does not require introduction of an infrared photon mass. The behavior of the diagrams containing radiative corrections near the mass shell is investigated, and it is shown that in the Fried-Yennie gauge this behavior is softer than in any other gauge and softer than the behavior of the corresponding graphs without radiative corrections
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
Fermions, gauge theories, and the Sinc function representation for Feynman diagrams
International Nuclear Information System (INIS)
Petrov, Dmitri; Easther, Richard; Guralnik, Gerald; Hahn, Stephen; Wang, Wei-Mun
2001-01-01
We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function representation for scalar field Feynman integrals are shared by fields with nonzero spin. We then investigate the application of the Sinc function representation to simple QED diagrams, including first order corrections to the propagators and the vertex
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.)
Feynman identity: A special case. I
International Nuclear Information System (INIS)
da Costa, G.A.
1997-01-01
There is an identity due to Feynman which relates graphs and closed curves on a lattice and it was used by Feynman in his combinatorial proof of Onsager close-quote s closed formula for the partition function of the two-dimensional Ising model. Long ago Sherman considered a special case of this identity and pointed out similarities with the Witt identity of Lie algebra theory. In this paper and following, we revisit this special case and solve some problems related with it. In particular, the weights are computed explicitly using paths and words and a direct connection with the Witt formula is found. copyright 1997 American Institute of Physics
The Errors of Feynman and Hibbs
Indian Academy of Sciences (India)
It is not known exactly when work on the book com- menced. Feynman started work at CalTech on 1 July. 1950[4, p.332]. On 30 December 1952 the television show `You Bet Your Life' (Season 1, Episode 3) aired an interview with Hibbs in which he said he's working on a book to be titled Quantum Mechanics and Path In-.
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.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. Richard P Feynman (1918-1988). Featured Scientist Volume 16 Issue 9 September 2011 pp 908-908. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/016/09/0908-0908. Resonance – Journal of ...
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
The Errors of Feynman and Hibbs
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. The Errors of Feynman and Hibbs. Daniel F Styer. General Article Volume 16 Issue 9 September 2011 pp 849-853. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/016/09/0849-0853. Keywords.
Dual Feynman rules - topological asymptotic freedom
International Nuclear Information System (INIS)
Chew, G.F.; Levinson, M.; California Univ., Berkeley
1983-01-01
Feynman-graph rules are formulated for the strong - interaction components of the topological expansion - defined as those graphs all of whose vertices are zero - entropy connected parts. These rules imply a ''topological asymptotic freedom'' and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry. (orig.)
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
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
Energy Technology Data Exchange (ETDEWEB)
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew
2015-07-01
In his legendary lectures from the year 1965 Richard P. feynman succeeded in representing physics in an easily understandable form without abandoning accuracy. The didactically clever construction keeps the reader tide to the end. It is no wonder, then, that Feynman's lectures on physics have now taken a firm place in the teaching enterprise of the universities. This book is excellently suited for the self-study or as companion of a lecture. Volume 5 of the revised New Millenium Edition is dedicated to quantum mechanics and offers an excellent introduction to the theme, whereby all essential terms are treated with an extensive discussion.
A single-loop recombinant pseudotyped-virus-based assay to detect HIV-1 phenotypic resistance.
Wu, Shouli; Yan, Pingping; Yan, Yansheng; Qiu, Lijun; Xie, Meirong
2015-06-01
HIV/AIDS is a leading public health concern throughout the world. Currently, treatment of HIV/AIDS still depends on highly active antiretroviral therapy (HAART); however, there is increasing evidence showing the emergence of resistance to antiretroviral drugs in HIV-1 strains, making ART less effective over time. Intensive monitoring of HIV-1 drug resistance is therefore of great importance to evaluate the current sensitivity of antiretroviral agents and is urgently needed. The aim of this study was to develop a single-loop recombinant pseudotyped-virus-based assay to detect phenotypic resistance in clinical HIV-1 strains. HIV-1 RNA was extracted from HIV-1-infected human plasma samples, and an approximately 3-kb fragment containing p7/p1/p6 cleavage sites and full-length protease (PR), reverse transcriptase (RT), thermonuclease (TNase), and integrase (1-280 aa) genes was amplified by nested RT-PCR. A retroviral vector was constructed using the HIV-1 infectious molecular clone pLWJ to test antiretroviral drug susceptibility. pLWJ-SV40-Luc contained a luciferase expression cassette inserted within a deleted region of the envelope (env) gene as an indicator gene. Resistance test vectors (RTVs) were constructed by incorporating amplified target genes into pLWJ-SV40-Luc by using ApaI or AgeI and AarI restriction sites and conventional cloning methods. The virus stocks used for drug susceptibility test were produced by co-transfecting 293T cells with RTVs and a plasmid that provided vesicular stomatitis virus glycoprotein (VSV-G). Viral replication was monitored by measuring luciferase activity in infected target cells at approximately 48 h postinfection. A total of 35 clinical plasma samples from HIV-1-infected humans were tested, and target fragments were successfully amplified from 34 samples (97.1 %) and 33 RTVs were successfully constructed by directional cloning, with an overall success rate of 94.3 %. A clear-cut dose-dependent relationship was detected between
Reiff, Patricia H.; Feynman, Joan; Gold, Thomas; Wasserburg, G. J.; Sheeley, Neil R., Jr.; Akasofu, S.-I.
1988-01-01
Richard Feynman, simply put, was a genius. His quick wit and uncommon grasp of physics meant that any research area he encountered, he quickly mastered. Despite the fact that his own area of research was not geophysics, his life and work influenced almost all of us. Virtually every physics graduate student who started in the mid 60s or later was exposed to his Lectures on Physics, either by having them as a text for a course or by using them (as I did) to bone up for oral qualifying exams...
A practical guide to Feynman diagrams
International Nuclear Information System (INIS)
Bowler, K.C.
1980-01-01
These lectures serve as an introduction to the basic ideas of relativistic quantum theory, perturbation theory and the Feynman diagram calculus, in the context of electromagnetic interactions. The main objective is to get the student as rapidly as possible to the point where he can calculate the lowest order cross-sections for a variety of two-body electromagnetic processes. The techniques are considered under the headings: relativistic wave equations, electrodynamics of spinless particles, and electrodynamics of spin-1/2 particles. A selection of problems and exercises is included. (U.K.)
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
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''
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.
Fanaro, Maria de los Angeles; Arlego, Marcelo; Otero, Maria Rita
2012-01-01
This work comprises an investigation about basic Quantum Mechanics (QM) teaching in the high school. The organization of the concepts does not follow a historical line. The Path Integrals method of Feynman has been adopted as a Reference Conceptual Structure that is an alternative to the canonical formalism. We have designed a didactic sequence…
Feynman's lost lecture the motion of planet's around the sun
Goodstein, David L
1997-01-01
On 14 March 1964 Richard Feynman, one of the greatest scientific thinkers of the 20th Century, delivered a lecture entitled 'The Motion of the Planets Around the Sun'. For thirty years this remarkable lecture was believed to be lost. But now Feynman's work has been reconstructed and explained in meticulous, accessible detail, together with a history of ideas of the planets' motions. The result is a vital and absorbing account of one of the fundamental puzzles of science, and an invaluable insight into Feynman's charismatic brilliance.
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
Toolbox for multiloop Feynman diagrams calculations using $R^{*}$ operation
Batkovich, Dmitrii; Kompaniets, Mikhail
2014-01-01
We present the toolbox for analytical calculation of UV-counterterm of Feynman diagrams. It combines the power of $R^{*\\prime}$-operation with modern analytical methods. Written in pure Python our toolbox can be easily used and extended.
Two-loop renormalization of Feynman gauge QED
International Nuclear Information System (INIS)
Adkins, Gregory S.; Fell, Richard N.; Sapirstein, J.
2001-01-01
We calculate the two-loop renormalization constants deltam, Z 1 , and Z 2 in Feynman gauge QED using dimensional regularization to control ultraviolet divergences and a non-zero photon mass to regulate infrared divergences
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.)
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
Feynman lectures on physics 5. Quantum mechanics. 6. ed.
International Nuclear Information System (INIS)
Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew
2015-01-01
In his legendary lectures from the year 1965 Richard P. feynman succeeded in representing physics in an easily understandable form without abandoning accuracy. The didactically clever construction keeps the reader tide to the end. It is no wonder, then, that Feynman's lectures on physics have now taken a firm place in the teaching enterprise of the universities. This book is excellently suited for the self-study or as companion of a lecture. Volume 5 of the revised New Millenium Edition is dedicated to quantum mechanics and offers an excellent introduction to the theme, whereby all essential terms are treated with an extensive discussion.
Quadratic Feynman loop integrands from massless scattering equations
Gomez, Humberto
2017-05-01
Recently, the Cachazo-He-Yuan (CHY) approach has been extended to the loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this paper, we present a new technique that directly produces quadratic propagators identical to Feynman's from the CHY approach. This paper focuses on the Φ3 theory, but extensions to other theories are briefly discussed. In addition, our proposal has an interesting geometric meaning; we can interpret this new formula as a unitary cut on a higher genus Riemann surface.
Feynman's thesis: A new approach to quantum theory
Energy Technology Data Exchange (ETDEWEB)
Das, Ashok [Department of Physics and Astronomy, University of Rochester (United States)
2007-01-07
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
Factorization of Feynman graphs at finite temperature and chemical potential
International Nuclear Information System (INIS)
Espinosa, Olivier
2007-01-01
I report on a recently discovered general property of Feynman diagrams in thermal field theories (Thermal Operator Representation): the thermal part of any diagram can be obtained directly from the vacuum part by means of a simple diagram-dependent linear operator with interesting properties
Five Things I Learned from Richard Feynman About Science ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. Five Things I Learned from Richard Feynman About Science Education. Kathy Ceceri. Personal Reflections Volume 16 Issue 9 September 2011 pp 879-880. Fulltext. Click here to view fulltext PDF. Permanent link:
Five Things I Learned from Richard Feynman About Science ...
Indian Academy of Sciences (India)
the committee which reported to Congress after the Space Shuttle Challenger disaster. It was. Feynman who dipped a rubber O-ring into a glass of ice water to show how it became brittle – a simple but devastating demonstration. His lectures at Caltech, which are still studied today in book form, are considered classics.
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.
Richard Phillips Feynman-Physicist and Teacher Extraordinary
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. Richard Phillips Feynman - Physicist and Teacher Extraordinary. N Mukunda. Article-in-a-Box Volume 16 Issue 9 September 2011 pp 796-797. Fulltext. Click here to view fulltext PDF. Permanent link:
To Have Been a Student of Richard Feynman
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 16; Issue 9. To Have Been a Student of Richard Feynman. Laurie M Brown. Personal Reflections Volume 16 Issue 9 September 2011 pp 874-878. Fulltext. Click here to view fulltext PDF. Permanent link:
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.
To Have Been a Student of Richard Feynman
Indian Academy of Sciences (India)
Feynman stressed creativity—which to him meant working things out from the beginning. He urged each of us to create his or her own universe of ideas, so that our products, even if only answers to assigned classwork problems, would have their own original charac- ter—just as his own work carried the unique stamp of his ...
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.
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-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.
Quantenmechanik im Kalten Krieg David Bohm und Richard Feynman
Forstner, Christian
2007-01-01
Mitte des 20. Jahrhunderts entwickelten David Bohm und Richard Feynman zwei grundlegend verschiedene Ansätze der moderne Quantenmechanik: Bohm eine realistische Deutung mit Hilfe verborgener Parameter und Feynman den Pfadintegralformalismus. Dies ist umso bemerkenswerter, weil beide Physiker von ähnlichen Voraussetzungen ausgingen und aus ähnlichen Zusammenhängen stammten. Durch ihren vergleichenden Ansatz bietet diese Studie mehr als einen Beitrag zur Geschichte der Quantentheorie. Mit der Frage nach den sozialen und kulturellen Bedingungen der Theoriebildung ist sie darüberhinaus von wissenschaftssoziologischem und wissenschaftstheoretischem Interesse. Die anfangs ähnliche und später unterschiedliche Einbindung der beiden Wissenschaftler in die Scientific Community erlaubt es überdies zu untersuchen, welchen Anpassungsdruck die jeweilige Gruppe auf den individuellen Wissenschaftler und die Kernbestandteile seiner Forschungen ausübt und welche neuen Freiheitsgrade für die Theoriebildung entstehen, ...
The Feynman iɛ in string theory
Witten, Edward
2015-04-01
The Feynman iɛ is an important ingredient in defining perturbative scattering amplitudes in field theory. Here we describe its analog in string theory. Roughly one takes the string worldsheet to have Lorentz signature when a string is going on-shell although it has Euclidean signature generically. (This article is based on a talk presented at the Zuminofest in Berkeley, California, May 2-4, 2013.)
The Feynman iε in string theory
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Witten, Edward [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ 08540 (United States)
2015-04-13
The Feynman iε is an important ingredient in defining perturbative scattering amplitudes in field theory. Here we describe its analog in string theory. Roughly one takes the string worldsheet to have Lorentz signature when a string is going on-shell although it has Euclidean signature generically. (This article is based on a talk presented at the Zuminofest in Berkeley, California, May 2-4, 2013.)
Some remarks on non-planar Feynman diagrams
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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.
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.
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
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.
International Nuclear Information System (INIS)
Inazumi, T.; Bell, G.E.C.; Kenik, E.A.; Kiuchi, K.
1993-01-01
Single-loop electrochemical potentiokinetic reactivation testing of miniaturized (TEM) specimens can provide reliable data comparable to data obtained with larger specimens. Significant changes in electrochemical properties (increased reactivation current and Flade potential) were detected for PCA and type 316 stainless steels irradiated at 200--420 degrees C up to 7--9 dpa. Irradiations in the FFTF Materials Open Test Assembly and in the Oak Ridge Research Reactor are reported on. 45 figs., 5 tabs., 52 refs
FeynEdit—a tool for drawing Feynman diagrams
Hahn, T.; Lang, P.
2008-12-01
We describe the FeynEdit tool for drawing Feynman diagrams. Input and output is done using the ? macros of FeynArts, which also implies that diagrams drawn by FeynArts can be edited with FeynEdit. The ? code can be conveniently transferred using copy-and-paste. Program summaryProgram title: FeynEdit Catalogue identifier: AEBX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 31 729 No. of bytes in distributed program, including test data, etc.: 500 240 Distribution format: tar.gz Programming language: Java Computer: All Java-capable platforms Operating system: Linux, Mac OS, Windows RAM: 1-2 MBytes Classification: 4.4 Nature of problem: Graphical editing of Feynman diagrams. Solution method: The user copy-and-pastes the LaTeX code of the Feynman diagram into the editor, clicks a button to visualize the diagram, modifies it using the mouse, and finally copy-and-pastes it back into the text. Restrictions: Propagators are presently drawn only as straight lines. This is largely for performance reasons and may be added in a future version. It is not a serious deficit because that information can easily be added in the LaTeX code. Unusual features: Uses FeynArts' LaTeX representation for input and output Running time: User-dependent
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
Functional integration and quantum physics
Simon, Barry
2004-01-01
The main theme of this book is the "path integral technique" and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the Feynman-Kac formula. Starting with the main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman-Kac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman-Kac-Itô formula). Among other topics
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.
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.
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.)
Introduction to LINE: a Feynman diagram graphic generator
International Nuclear Information System (INIS)
LeClaire, B.
1985-03-01
This is an exec for making Feynman graphs of amazing complexity with amazing simplicity - once you know how. And knowing how is hopefully quite easy to learn. The LINE exec works iteratively, repeatedly prompting you for the elements of the graph. You tell the exec what kinds of lines (or loops) to draw, and where to put them. Each line is plotted in a 10 x 10 Cartesian coordinate system using two ordered pairs of coordinates, (x 1 ,y 1 ) and (x 2 ,y 2 ), as endpoints. The types of lines that can be drawn include fermions, scalars, photons, gluons, W or Z bosons. As each line is added the exec alows you to display the updated picture, and to erase the last line added (if necessary). In this way you can keep going, drawing and erasing, until you have exactly what you want
You err, Einstein.. Newton, Einstein, Heisenberg, and Feynman discuss quantum physics
International Nuclear Information System (INIS)
Fritzsch, Harald
2008-01-01
Harald Fritzsch and his star physicists Einstein, Heisenberg, and Feynman explain the central concept of nowadays physics, quantum mechanics, without it nothing goes in modern world. And the great Isaac newton puts the questions, which all would put
The calculation of QCD triangular Feynman graphs in external gluonic field using the Reduce-2 system
International Nuclear Information System (INIS)
Dulyan, L.S.
1986-01-01
Methods and ways applied in the calculation of the QCD triangular Feynman diagrams with the use of the REDUCE-2 system are described. The encountered difficulties connected with the specific features of the REDUCE-2 system are discussed
Why Professor Richard Feynman was upset solving the Laplace equation for spherical waves?
Khelashvili, Anzor; Nadareishvili, Teimuraz
2013-01-01
We take attention to the singular behavior of the Laplace operator in spherical coordinates, which was established in our earlier work. This singularity has many non-trivial consequences. In this article we consider only the simplest ones, which are connected to the solution of Laplace equation in Feynman classical books and Lectures. Feynman was upset looking in his derived solutions, which have a fictitious singular behavior at the origin. We show how these inconsistencies can be avoided.
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
Energy Technology Data Exchange (ETDEWEB)
Ochman, Michal; Riemann, Tord
2015-11-15
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.
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
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)
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.
HELAS: HELicity Amplitude Subroutines for Feynman diagram evaluations
International Nuclear Information System (INIS)
Murayama, H.; Watanabe, I.; Hagiwara, K.
1992-01-01
HELAS is a set of the FORTRAN 77 subroutines which enable to compute the helicity amplitude of an arbitrary tree level Feynman diagram with a simple sequence of CALL SUBROUTINE statements. It is easy to write down a FORTRAN program to calculate the helicity amplitude of a given process by calling the HELAS subroutines. The example of evaluating the helicity amplitude of the process W + W - →t anti-t is shown. The compactness of the helicity amplitude programs is the main advantage of using the HELAS. Another advantage is that it is very easy to allow external heavy particles to decay into light quarks and leptons without losing the spin correlation. The procedure of calculating the cross section of an arbitrary process with the help of the HELAS and noteworthy characteristics of the HELAS system are shown. How to use the HELAS package is explained about the above example. The HELAS subroutines are grouped in wave functions, nine vertices and tools and standard model coupling constants. HELAS CHECK messages makes the job to find mistake easy. (K.I.)
Gluon saturation and Feynman scaling in leading neutron production
Directory of Open Access Journals (Sweden)
F. Carvalho
2016-01-01
Full Text Available In this paper we extend the color dipole formalism for the study of leading neutron production in e+p→e+n+X collisions at high energies and estimate the related observables which were measured at HERA and could be analyzed in future electron–proton (ep colliders. In particular, we calculate the Feynman xF distribution of leading neutrons, which is expressed in terms of the pion flux and the photon–pion total cross section. In the color dipole formalism, the photon–pion cross section is described in terms of the dipole–pion scattering amplitude, which contains information about the QCD dynamics at high energies and gluon saturation effects. We consider different models for the scattering amplitude, which have been used to describe the inclusive and diffractive ep HERA data. Moreover, the model dependence of our predictions with the description of the pion flux is analyzed in detail. We demonstrate the recently released H1 leading neutron spectra can be described using the color dipole formalism and that these spectra could help us to observe more clearly gluon saturation effects in future ep colliders.
Fractional Feynman-Kac equation for weak ergodicity breaking.
Carmi, Shai; Barkai, Eli
2011-12-01
The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, ψ(τ) ~ τ(-(1+α)), leads to subdiffusion (x(2) ~ t(α)) for 0 CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for t → ∞ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for α = 1, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.
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.)
Thinking in Pictures: John Wheeler, Richard Feynman and the Diagrammatic Approach to Problem Solving
Halpern, Paul
While classical mechanics readily lends itself to sketches, many fields of modern physics, particularly quantum mechanics, quantum field theory, and general relativity, are notoriously hard to envision. Nevertheless, John Wheeler and Richard Feynman, who obtained his PhD under Wheeler, each insisted that diagrams were the most effective way to tackle modern physics questions as well. Beginning with Wheeler and Feynman's work together at Princeton, I'll show how the two influenced each other and encouraged each other's diagrammatic methods. I'll explore the influence on Feynman of not just Wheeler, but also of his first wife Arline, an aspiring artist. I'll describe how Feynman diagrams, introduced in the late 1940s, while first seen as `heretical' in the face of Bohr's complementarity, became standard, essential methods. I'll detail Wheeler's encouragement of his colleague Martin Kruskal's use of special diagrams to elucidate the properties of black holes. Finally, I'll show how each physicist supported art later in life: Wheeler helping to arrange the Putnam Collection of 20th century sculpture at Princeton and Feynman, in a kind of `second career,' becoming an artist himself.
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...
Vos, E.K.; Sambandamurthy, S.; Kamel, M.; McKenney, R.; Uden, M.J. van; Hoeks, C.M.A.; Yakar, D.; Scheenen, T.W.J.; Futterer, J.J.
2014-01-01
The objectives of this study were to test the feasibility of an investigational dual-channel next-generation endorectal coil (NG-ERC) in vivo, to quantitatively assess signal-to-noise ratio (SNR), and to get an impression of image quality compared with the current clinically available single-loop
Ilinca, A.; Mangini, D.; Mameli, M.; Fioriti, D.; Filippeschi, S.; Araneo, L.; Roth, N.; Marengo, M.
2017-11-01
A Novel Single Loop Pulsating Heat Pipe (SLPHP), with an inner diameter of 2 mm, filled up with two working fluids (Ethanol and FC-72, Filling Ratio of 60%), is tested in Bottom Heated mode varying the heating power and the orientation. The static confinement diameter for Ethanol and FC-72, respectively 3.4 mm and 1.7mm, is above and slightly under the inner diameter of the tube. This is important for a better understanding of the working principle of the device very close to the limit between the Loop Thermosyphon and Pulsating Heat Pipe working modes. With respect to previous SLPHP experiments found in the literature, such device is designed with two transparent inserts mounted between the evaporator and the condenser allowing direct fluid flow visualization. Two highly accurate pressure transducers permit local pressure measurements just at the edges of one of the transparent inserts. Additionally, three heating elements are controlled independently, so as to vary the heating distribution at the evaporator. It is found that peculiar heating distributions promote the slug/plug flow motion in a preferential direction, increasing the device overall performance. Pressure measurements point out that the pressure drop between the evaporator and the condenser are related to the flow pattern. Furthermore, at high heat inputs, the flow regimes recorded for the two fluids are very similar, stressing that, when the dynamic effects start to play a major role in the system, the device classification between Loop Thermosyphon and Pulsating Heat Pipe is not that sharp anymore.
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
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)
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.)
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.)
International Nuclear Information System (INIS)
Njock, Kwato M.G.; Nsangou, M.; mnsangouQuyedc.umnet.cm; Ournarou, B.; Boyomo, Onana M.
2002-06-01
The nonrelativistic hypervirial Hellmann-Feynman method developed recently is extended to deal with relativistic particles bound in a spherically symmetric potential. A simple analytical procedure for calculating correction terms of arbitrary high orders is derived. Numerical results obtained through a study of the screened Coulomb potential enable us to illustrate the improvements of our procedure over the previous approaches. (author)
International Nuclear Information System (INIS)
El Naschie, M.S.
2007-01-01
A fuzzy version of a great icosahedra-like platonic solid is used in conjunction with a Feynman diagram-polyhedron analogy to determine the number of elementary particles in the standard model of high energy physics which we define as a sub Yang-Mills model
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
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
Field, J. H.
2013-11-01
The five laws of relativistic quantum mechanics, according to Feynman's path integral formulation, are concisely stated and applied to experiments. Reflection-diffraction-grating experiments for both photons and electrons are analysed, in particular, the Davisson-Germer experiment in which the wave-like property of electrons was first established. It is shown how classical, purely spatial, effective wave theories for both photons and electrons are predicted by the path integral formulation of quantum mechanics. The standard Copenhagen interpretation of wave mechanics is critically discussed in the light of the described experimental applications of the path integral formulation.
Andreev, V.; Begzsuren, K.; Belousov, A.; Belov, P.; Boudry, V.; Brandt, G.; Brinkmann, M.; Brisson, V.; Britzger, D.; Buniatyan, A.; Bylinkin, A.; Bystritskaya, L.; Campbell, A.J.; Cantun Avila, K.B.; Ceccopieri, F.; Cerny, K.; Chekelian, V.; Contreras, J.G.; Dainton, J.B.; Daum, K.; Diaconu, C.; Dobre, M.; Dodonov, V.; Dossanov, A.; Eckerlin, G.; Egli, S.; Elsen, E.; Favart, L.; Fedotov, A.; Feltesse, J.; Ferencei, J.; Fleischer, M.; Fomenko, A.; Gabathuler, E.; Gayler, J.; Ghazaryan, S.; Glazov, A.; Goerlich, L.; Gogitidze, N.; Gouzevitch, M.; Grab, C.; Grebenyuk, A.; Greenshaw, T.; Grindhammer, G.; Haidt, D.; Henderson, R.C.W.; Herbst, M.; Hladky, J.; Hoffmann, D.; Horisberger, R.; Hreus, T.; Huber, F.; Jacquet, M.; Janssen, X.; Jung, H.; Kapichine, M.; Kiesling, C.; Klein, M.; Kleinwort, C.; Kogler, R.; Kostka, P.; Kretzschmar, J.; Kruger, K.; Landon, M.P.J.; Lange, W.; Laycock, P.; Lebedev, A.; Levonian, S.; Lipka, K.; List, B.; List, J.; Lobodzinski, B.; Lytkin, L.; Malinovski, E.; Martyn, H.U.; Maxfield, S.J.; Mehta, A.; Meyer, A.B.; Meyer, H.; Meyer, J.; Mikocki, S.; Morozov, A.; Muller, K.; Naumann, Th.; Newman, P.R.; Niebuhr, C.; Nowak, G.; Nowak, K.; Olsson, J.E.; Ozerov, D.; Pahl, P.; Pascaud, C.; Patel, G.D.; Perez, E.; Petrukhin, A.; Picuric, I.; Pirumov, H.; Pitzl, D.; Placakyte, R.; Pokorny, B.; Polifka, R.; Povh, B.; Radescu, V.; Raicevic, N.; Ravdandorj, T.; Reimer, P.; Rizvi, E.; Robmann, P.; Roosen, R.; Rostovtsev, A.; Rotaru, M.; Rusakov, S.; Salek, D.; Sankey, D.P.C.; Sauter, M.; Sauvan, E.; Schmitt, S.; Schoeffel, L.; Schoning, A.; Schultz-Coulon, H.C.; Sefkow, F.; Shushkevich, S.; Soloviev, Y.; Sopicki, P.; South, D.; Spaskov, V.; Specka, A.; Steder, M.; Stella, B.; Straumann, U.; Sykora, T.; Thompson, P.D.; Traynor, D.; Truol, P.; Tsakov, I.; Tseepeldorj, B.; Turnau, J.; Valkarova, A.; Vallee, C.; Van Mechelen, P.; Vazdik, Y.; Wegener, D.; Wunsch, E.; Zacek, J.; Zhang, Z.; Zlebcik, R.; Zohrabyan, H.; Zomer, F.
2014-06-24
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 $131 \\mathrm{pb}^{-1}$. The measurement is restricted to photons and neutrons in the pseudorapidity range $\\eta>7.9$ and covers the range of negative four momentum transfer squared at the positron vertex $6Feynman scaling hypothesis the $W$ dependence of the $x_F$ 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.
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.)
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)
Imaeda, K.; Imaeda, M.
1982-01-01
The classical Wheeler-Feynman absorber theory with a postulate of Lorentz-invariant zero-point electromagnetic radiation is proposed to explain quantum phenomena in a similar manner to that of stochastic electrodynamics. For this purpose, Cramer's model (Phys. Rev.; D22:362 (1980)) of a 'minimum emitter-absorber transaction' is extended to the case where zero-point radiation exists, in the context of the classical Wheeler-Feynman theory. The Einstein-Podolski-Rosen paradox and the quantum levels of a charged simple harmonic oscillator are derived from the theory. It is shown that the condition for a transaction plays an essential role, such as in the radiative balance of a simple harmonic oscillator. (author)
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 ...
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)
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
Path-integral derivation of the complex ABCD Huygens integral
International Nuclear Information System (INIS)
Wright, E.M.; Garrison, J.C.
1987-01-01
The Huygens integral, or Green's function, for paraxial beam propagation in a generalized lenslike medium is derived as a Feynman path integral involving a summation over real rays. This formulation provides a physically intuitive understanding of the structure of the Green's function. The path integral is evaluated by introducing in a consistent manner the notion of complex rays, and the familiar result for the Huygens integral in terms of the complex ABCD matrix of the medium is obtained
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
Path integrals as discrete sums
Bitar, Khalil; Khuri, N. N.; Ren, H. C.
1991-08-01
We present a new formulation of Feynman's path integral, based on Voronin's theorems on the universality of the Riemann zeta function. The result is a discrete sum over ``paths,'' each given by a zeta function. A new measure which leads to the correct quantum mechanics is explicitly given.
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.
Bogner, Christian; Schweitzer, Armin; Weinzierl, Stefan
2017-09-01
We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve. We show that all what is required is just the analytic continuation of these two periods. We present an explicit formula for the two periods for all values of t ∈ R. Furthermore, the nome q of the elliptic curve satisfies over the complete range in t the inequality | q | ≤ 1, where | q | = 1 is attained only at the singular points t ∈ {m2 , 9m2 , ∞ }. This ensures the convergence of the q-series expansion of the ELi-functions and provides a fast and efficient evaluation of these Feynman integrals.
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.)
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
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.
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
How I Got to Work with Feynman on the Covariant Quark Model
Ravndal, Finn
2015-03-01
In the period 1968-1974 I was a graduate student and then a postdoc at Caltech and was involved with the developments of the quark and parton models. Most of this time I worked in close contact with Richard Feynman and thus was present from the parton model was proposed until QCD was formulated. A personal account is presented how the collaboration took place and how the various stages of this development looked like from the inside until QCD was established as a theory for strong interactions with the partons being quarks and gluons.
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)
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
Topologically distinct Feynman diagrams for mass operator in electron-phonon interaction
Directory of Open Access Journals (Sweden)
C.C. Tovstyuk
2009-01-01
Full Text Available The new method for designing topologically distinct Feynman diagrams for electron's mass operator in electron-phonon interaction is developed using the permutation group theory. The carried out classification of DPs allows to choose the classes, corresponding to disconnected diagrams, to singly connected diagrams, direct ("tadpole" diagrams, to diagrams corresponding to phonon Green functions. After this classification the set of considered double permutations is reduced to one class since only these are relevant to mass operator. We derive analytical expressions which allow to identify the DP, and to choose the phonon components, which are not accepted in every type. To avoid repetition of asymmetric diagrams, which correspond to the same analytical expression, we introduce the procedure of inversion in phonon component, and identify symmetric as well as a pair of asymmetric phonon components. For every type of DP (denoted by its digital encoding, taking into account its symmetry, we perform a set of transformations on this DP, list all DPs of the type and all the corresponding Feynman diagrams of mass operator automatically. It is clear that no more expressions (diagrams for the relevant order of perturbation theory for mass operator can be designed.
International Nuclear Information System (INIS)
Lukaszuk, L.
1989-01-01
The problem of finding scattering amplitudes in the high energy, large momentum transfer limit is reconsidered. We propose a novel technique of evaluating Feynman diagrams in this regime with higher order perturbative corrections in mind. The relation to other methods is discussed and the ladder diagrams in φ 3 theory, recalculated up to sixth order, serve as examples. (orig.)
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
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.
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
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.
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.
Using an atom interferometer to take the Gedanken out of Feynman's Gedankenexperiment
International Nuclear Information System (INIS)
Pritchard, David E.; Hammond, Troy D.; Lenef, Alan; Rubenstein, Richard A.; Smith, Edward T.; Chapman, Michael S.; Schmiedmayer, Joerg
1997-01-01
We give a description of two experiments performed in an atom interferometer at MIT. By scattering a single photon off of the atom as it passes through the interferometer, we perform a version of a classic gedankenexperiment, a demonstration of a Feynman light microscope. As path information about the atom is gained, contrast in the atom fringes (coherence) is lost. The lost coherence is then recovered by observing only atoms which scatter photons into a particular final direction. This paper reflects the main emphasis of D. E. Pritchard's talk at the RIS meeting. Information about other topics covered in that talk, as well as a review of all of the published work performed with the MIT atom/molecule interferometer, is available on the world wide web at http://coffee.mit.edu/
On the applicability of the pulsing Feynman-{alpha} method: Validation with MUSE experiments
Energy Technology Data Exchange (ETDEWEB)
Ballester, D. [Department of Chemical and Nuclear Engineering, Polytechnic University of Valencia, Cami de Vera s/n, 46022 Valencia (Spain)]. E-mail: dabalber@iqn.upv.es; Munoz-Cobo, J.L. [Department of Chemical and Nuclear Engineering, Polytechnic University of Valencia, Cami de Vera s/n, 46022 Valencia (Spain)]. E-mail: jlcobos@iqn.upv.es; Kloosterman, J.L. [Interfaculty Reactor Institute, Department of Reactor Physics, Delft University of Technology, Mekelweg 15, 2629 JB Delft (Netherlands)]. E-mail: kloosterman@iri.tudelft.nl
2005-09-15
We investigate the application of the Feynman-{alpha} method using an external pulsed source as a subcriticality level monitoring technique. The influence of the non-Poissonian nature of the pulsed source and the presence of the intrinsic spontaneous fission source are considered. Experimental data gathered during the MUSE-4 European project for different nuclear assembly conditions are reported and applied to fit the system prompt neutron time constant within the fundamental mode approach, 1/(-{alpha} {sub 0}), with theoretical expressions previously obtained. Experiments show that, under certain circumstances, the deterministic character of the external pulsed source makes the system to behave as a sub-Poissonian one. In addition, the stochastic pulsing method seems to be more adequate than the deterministic one because the number of fitting parameters is lower, and also due to its better statistical behaviour for the given experimental conditions.
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)
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.
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.)
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)
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
On the Schwinger-De Witt expansion for the Feynman propagator in a curved space-time
International Nuclear Information System (INIS)
John, R.W.
1986-01-01
The Feynman propagator in curved space-time is defined in a manifestly covariant way by the help of the Schwinger-De Witt representation. Building elements of the Schwinger-De Witt expansion are obtained on a model space-time being of non-constant curvature and yielding not identically vanishing Hadamard coefficients. The world function can be calculated exactly and in closed form for special representatives of highly symmetric space-time only
Chernikova, Dina; Axell, Kåre; Avdic, Senada; Pázsit, Imre; Nordlund, Anders; Allard, Stefan
2015-05-01
Two versions of the neutron-gamma variance to mean (Feynman-alpha method or Feynman-Y function) formula for either gamma detection only or total neutron-gamma detection, respectively, are derived and compared in this paper. The new formulas have particular importance for detectors of either gamma photons or detectors sensitive to both neutron and gamma radiation. If applied to a plastic or liquid scintillation detector, the total neutron-gamma detection Feynman-Y expression corresponds to a situation where no discrimination is made between neutrons and gamma particles. The gamma variance to mean formulas are useful when a detector of only gamma radiation is used or when working with a combined neutron-gamma detector at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with the inclusion of general reactions and corresponding intensities for neutrons and gammas, but with the inclusion of prompt reactions only. A one energy group approximation is considered. The comparison of the two different theories is made by using reaction intensities obtained in MCNPX simulations with a simplified geometry for two scintillation detectors and a 252Cf-source. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma are evaluated experimentally for a weak 252Cf neutron-gamma source, a 137Cs random gamma source and a 22Na correlated gamma source. Due to the focus being on the possibility of using neutron-gamma variance to mean theories for both reactor and safeguards applications, we limited the present study to the general analytical expressions for Feynman-alpha formulas.
Charged Higgs boson mass of the MSSM in the Feynman diagrammatic approach
Frank, M.; Hahn, T.; Heinemeyer, S.; Hollik, W.; Rzehak, H.; Weiglein, G.
2013-01-01
The interpretation of the Higgs signal at $\\sim$ 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, $M_{H^{\\pm}}$. 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 $O(\\alpha_t\\alpha_s)$. The one-loop contributions lead to sizable shifts in the $M_H^{\\pm}$ prediction, reaching up to $\\sim$ 8 GeV for relatively small values of M_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 $O(\\alpha_t\\alpha_s)$ terms can shift $M_H^{\\pm}$ 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 effect...
International Nuclear Information System (INIS)
Packwood, Daniel M.; Oniwa, Kazuaki; Jin, Tienan; Asao, Naoki
2015-01-01
Organic crystals have unique charge transport properties that lie somewhere between delocalised band-type transport and localised hopping transport. In this paper, we use a stochastic tight-binding model to explore how dynamical disorder in organic crystals affects charge transport. By analysing the model in terms of Feynman diagrams (virtual processes), we expose the crucial role of correlated dynamical disorder to the charge transport dynamics in the model at short times in the order of a few hundred femtoseconds. Under correlated dynamical disorder, the random motions of molecules in the crystal allow for low-energy “bonding”-type interactions between neighboring molecular orbitals can persist over long periods of time. On the other hand, the dependence of charge transport on correlated dynamical disorder also tends to localize the charge, as correlated disorder cannot persist far in space. This concept of correlation may be the “missing link” for describing the intermediate regime between band transport and hopping transport that occurs in organic crystals
A New Look At The Path Integral Of Quantum Mechanics
Witten, Edward
2010-01-01
The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct explanation of the relationship of the A-model to quantum mechanics; such a relationship has been explored from several points of view in the last few years. These phenomena have an analog for Chern-Simons gauge theory in three dimensions: integration cycles...
Numerical calculation of path integrals : The small-polaron model
Raedt, Hans De; Lagendijk, Ad
1983-01-01
The thermodynamic properties of the small-polaron model are studied by means of a discrete version of the Feynman path-integral representation of the partition function. This lattice model describes a fermion interacting with a boson field. The bosons are treated analytically, the fermion
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.)
Efficient Calculation of Energy Expectation Values in the Path Integral Formalism
Grujic, J
2006-01-01
The path integral formalism, originally introduced by Richard Feynman, represents a powerful general framework for dealing with quantum and statistical theories, as well as an extremely useful tool in many other areas of science. Their numerical integration, however, is notoriously demanding of computer time and it is one of the most challenging computational problems.
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
International Nuclear Information System (INIS)
Ballester, Daniel; Munoz-Cobo, Jose L.
2005-01-01
Stochastic neutron transport theory is applied to the derivation of the Feynman-Y function for subcritical assemblies when external pulsed sources are used. We obtain a general relationship between the probability generating functions of the kernel and the source considering the contribution to the detector statistics of both the pulsed source and the intrinsic neutron source. An expansion in α-eigenvalues is derived for the final solution, which permits to take into account the effect of higher harmonics in subcritical systems. In addition, numerical calculations have been done for a proposed model problem to understand the applicability of the method studied
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...
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.)
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)
Vos, Eline K; Sambandamurthy, Sriram; Kamel, Maged; McKenney, Robert; van Uden, Mark J; Hoeks, Caroline M A; Yakar, Derya; Scheenen, Tom W J; Fütterer, Jurgen J
2014-01-01
The objectives of this study were to test the feasibility of an investigational dual-channel next-generation endorectal coil (NG-ERC) in vivo, to quantitatively assess signal-to-noise ratio (SNR), and to get an impression of image quality compared with the current clinically available single-loop endorectal coil (ERC) for prostate magnetic resonance imaging at both 1.5 and 3 T. The study was approved by the institutional review board, and written informed consent was obtained from all patients. In total, 8 consecutive patients with prostate cancer underwent a local staging magnetic resonance examination with the successive use of both coils in 1 session (4 patients at 1.5 T and 4 other patients at 3 T). Quantitative comparison of both coils was performed for the apex, mid-gland and base levels at both field strengths by calculating SNR profiles in the axial plane on an imaginary line in the anteroposterior direction perpendicular to the coil surface. Two radiologists independently assessed the image quality of the T2-weighted and apparent diffusion coefficient maps calculated from diffusion-weighted imaging using a 5-point scale. Improvement of geometric distortion on diffusion-weighted imaging with the use of parallel imaging was explored. Statistical analysis included a paired Wilcoxon signed rank test for SNR and image quality evaluation as well as κ statistics for interobserver agreement. No adverse events were reported. The SNR was higher for the NG-ERC compared with the ERC up to a distance of approximately 40 mm from the surface of the coil at 1.5 T (P image quality was considered better for NG-ERC at both field strengths. Quality of apparent diffusion coefficient maps with the use of parallel imaging was rated superior with the NG-ERC at 3 T. The investigational NG-ERC for prostate imaging outperforms the current clinically available ERC in terms of SNR and is feasible for continued development for future use as the next generation endorectal coil for
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
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
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.
International Nuclear Information System (INIS)
Onorato, P
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P Feynman and developed by E F Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of propagation amplitude is discussed for unbounded systems. These semiclassical results are obtained when the SOP is limited to the trajectories classically allowed. EBK semiclassical quantization and the topological Maslov index are used to deduce the correct quantum mechanical results for systems which live in a two-dimensional world as quantum dots and quantum rings. In the latter systems, the semiclassical propagation amplitude is used to discuss the Aharonov-Bohm effect. The development involves only elementary calculus and also provides a theoretical introduction to the quantum nature of low-dimensional nanostructures.
Energy Technology Data Exchange (ETDEWEB)
Ballester, D.; Munoz-Cobo, J.L. [Valencia Polytechnic Univ., Dept. of Chemical and Nuclear Engineering (Spain); Kloosterman, J.L. [Delft Univ. of Technology, Faculty of Applied Sciences, Physics of Nuclear Reactors (Netherlands)
2005-07-01
Stochastic neutron transport theory is applied to the derivation of the Feynman-Y function for subcritical assemblies when external pulsed sources are used. We obtain a general relationship between the probability generating functions of the kernel and the source considering the contribution to the detector statistics of both, the pulsed source and the intrinsic neutron source. Expressions corresponding to the fundamental mode approach are obtained. In addition, these expressions are used to fit the system prompt neutron time constant, 1/(-{alpha}{sub 0}), with experimental data gathered during the Muse-4 European project for different nuclear assembly conditions. Experiments show that, under certain circumstances, the deterministic character of the external pulsed source makes the system to behave as a sub-Poissonian one. In addition, the stochastic pulsing method seems to be more adequate than the deterministic one because of the lower number of fitting parameters, and its better statistical behavior for the given experimental conditions. (authors)
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.
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...
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
De Santo, Luca Salvatore; Bisaccia, Carmela; De Santo, Rosa Maria
2009-01-01
Water is a complex source of imagination, dreams and rituals, where cultural differences ebb and flow, where a plethora of meanings and interpretations interlink and wash over one another. Water has an ambivalent character as stated in most of the ancient cosmogonies and in the Epic of Gilgamesh. Water's composition was discovered by the London scientist Henry Cavendish in about 1781. Although it is an apparently simple molecule (H2O), it has a highly complex and anomalous character. The anomalous properties of water are those where the behavior of liquid water is quite different from what is found with other liquids. As often stated, life depends indeed on these anomalous properties of water. Notably there are 12 phase, 22 density, 12 material, 11 thermodynamic and 9 physical anomalies. A powerful look into the water molecule was given by Nobel Prize recipient Richard P. Feynman as published in Six easy pieces. A look into the most recent quest for more knowledge about water leads us to the concept of pathological science. The cases of "polywater" and "the memory of water" are indeed paradigmatic episodes of fraudulent research published in journals with high impact factors. In conclusion, men came out of water engineered to handle water, and water greatly affects mythology and philosophy and is a strong presence in the arts and science.
The path integral method in quantum field theory
International Nuclear Information System (INIS)
Burden, C.J.
1990-01-01
Richard Feynman is reputed to have once the that in his whole life he had only ever had two really clever ideas. As it has turned out, these two ideas, the path integral formulation of quantum mechanics and the diagrammatic representation of perturbation theory have become the cornerstone of modern quantum field theory and particle physics. The path integral, first hinted at by Dirac in the thirties but developed fully by Feynman in the late 40's provides us with an alternative, though equivalent, description of quantum mechanics to canonical quantization. It was not until the seventies that it found broad application in quantum field theory (QFT), leading of gauge theories. It has also lead to the invention of non-perturbative techniques such as lattice gauge theory and has revealed an intimate connection between QFT and statistical mechanics. This paper, the author develops the basic of QFT form the path integral formalism and introduce the idea of Feynman diagrams for calculating perturbation expansions. I will concentrate mainly on the example of φ 4 theory since it is probably the simplest example of an interacting field theory, though the methods generalize readily to more sophisticated theories
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
International Nuclear Information System (INIS)
Akaho, E.H.K.; Intsiful, J.D.K.; Maakuu, B.T.; Anim-Sampong, S.; Nyarko, B.J.B.
2002-01-01
Reactor noise analysis was carried out for Ghana Research Reactor-1 GHARR-1, a tank-in-pool type reactor using the Feynman-α technique (variance-to-mean method). Measurements made at different detector positions and under subcritical conditions showed that the technique could not be used to determine the prompt decay constant for the reactor which is Be reflected with photo-neutron background. However, for very low dwell times the technique was used to measure the dead time of the detector which compares favourably with the value obtained using the α-conventional method
Akaho, E H K; Intsiful, J D K; Maakuu, B T; Nyarko, B J B
2002-01-01
Reactor noise analysis was carried out for Ghana Research Reactor-1 GHARR-1, a tank-in-pool type reactor using the Feynman-alpha technique (variance-to-mean method). Measurements made at different detector positions and under subcritical conditions showed that the technique could not be used to determine the prompt decay constant for the reactor which is Be reflected with photo-neutron background. However, for very low dwell times the technique was used to measure the dead time of the detector which compares favourably with the value obtained using the alpha-conventional method.
Distributed and multi-core computation of 2-loop integrals
International Nuclear Information System (INIS)
De Doncker, E; Yuasa, F
2014-01-01
For an automatic computation of Feynman loop integrals in the physical region we rely on an extrapolation technique where the integrals of the sequence are obtained with iterated/repeated adaptive methods from the QUADPACK 1D quadrature package. The integration rule evaluations in the outer level, corresponding to independent inner integral approximations, are assigned to threads dynamically via the OpenMP runtime in the parallel implementation. Furthermore, multi-level (nested) parallelism enables an efficient utilization of hyperthreading or larger numbers of cores. For a class of loop integrals in the unphysical region, which do not suffer from singularities in the interior of the integration domain, we find that the distributed adaptive integration methods in the multivariate PARINT package are highly efficient and accurate. We apply these techniques without resorting to integral transformations and report on the capabilities of the algorithms and the parallel performance for a test set including various types of two-loop integrals
AZURITE : An algebraic geometry based package for finding bases of loop integrals
Georgoudis, Alessandro; Larsen, Kasper J.; Zhang, Yang
2017-12-01
For any given Feynman graph, the set of integrals with all possible powers of the propagators spans a vector space of finite dimension. We introduce the package AZURITE (A ZUR ich-bred method for finding master I nTE grals), which efficiently finds a basis of this vector space. It constructs the needed integration-by-parts (IBP) identities on a set of generalized-unitarity cuts. It is based on syzygy computations and analyses of the symmetries of the involved Feynman diagrams and is powered by the computer algebra systems SINGULAR and MATHEMATICA. It can moreover analytically calculate the part of the IBP identities that is supported on the cuts. In some cases, the basis obtained by AZURITE may be slightly overcomplete.
Hoch, Michael
2017-01-01
Andy Charalambous; art@andycharalambous.com artist and trained engineer based in London UK, HEP Artist in Residence, Astronomy Artist in Residence and Honorary Research Fellow Physics and Astronomy University College London http://www.andycharalambous.com art@CMS_sciARTbooklet: web page : http://artcms.web.cern.ch/artcms/ A tool to support students with their research on various scientific topics, encourage an understanding of the relevance of expression through the arts, a manual to recreate the artwork and enable students to define and develop their own artistic inquiry in the creation of new artworks. The art@CMS sciART booklet series directed by Dr. Michael Hoch, michael.hoch@cern.ch scientist and artist at CERN, in cooperation with the HST 2017 participants (S. Bellefontaine, S. Chaiwan, A. Djune Tchinda, R. O’Keeffe, G. Shumanova)
On the Numerical Solution of the Integral Equation Formulation for Transient Structural Synthesis
2014-09-01
Keenan L. Coleman Lieutenant, United States Navy B.S., University of Arizona, 2007 Submitted in partial fulfillment of the requirements for...history of integral equations dates back to the early nineteenth century when the profound mathematical insights of Newton and Leibniz were being...Neta for their guidance and patience during this process. Finally, I would like to thank Dr. Richard Feynman, whose marriage of genius and common
Reduction method for one-loop tensor 5- and 6-point integrals revisited
International Nuclear Information System (INIS)
Diakonidis, Theodoros
2009-01-01
A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)
One-loop tensor integrals in dimensional regularisation
International Nuclear Information System (INIS)
Campbell, J.M.; Glover, E.W.N.; Miller, D.J.
1997-01-01
We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of n- and (n-1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to the external parameters - essentially yielding scalar integrals with Feynman parameters in the numerator - or by developing the scalar integral in D=6-2ε or higher dimensions. An additional advantage is that other spurious kinematic singularities are also controlled. As an explicit example, we develop the tensor integrals and associated scalar integral combinations for processes where the internal particles are massless and where up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals. (orig.)
Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms
Bourjaily, Jacob L.; McLeod, Andrew J.; Spradlin, Marcus; von Hippel, Matt; Wilhelm, Matthias
2018-03-01
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.
Investigation of speed estimation using single loop detectors.
2008-05-15
The ability to collect or estimate accurate speed information is of great importance to a large number of : Intelligent Transportation Systems (ITS) applications. Estimating speeds from the widely used single : inductive loop sensor has been a diffic...
Length based vehicle classification on freeways from single loop detectors.
2009-10-15
Roadway usage, particularly by large vehicles, is one of the fundamental factors determining the lifespan : of highway infrastructure, e.g., as evidenced by the federally mandated Highway Performance : Monitoring System (HPMS). But the complexity of ...
Malgieri, Massimiliano; Tenni, Antonio; Onorato, Pasquale; De Ambrosis, Anna
2016-09-01
In this paper we present a reasoning line for introducing the Pauli exclusion principle in the context of an introductory course on quantum theory based on the sum over paths approach. We start from the argument originally introduced by Feynman in ‘QED: The Strange Theory of Light and Matter’ and improve it by discussing with students modern experimental evidence from the famous Hong-Ou-Mandel experiment with indistinguishable photons and its generalised version using electrons. The experiments can be analysed in a rather simple way using Feynman’s method of ‘arrow multiplication’ for treating processes involving more than one quantum object. The approach described is especially relevant in the formation of high school physics teachers to the basics of modern physics.
International Nuclear Information System (INIS)
Gutlé, Claudine
2017-01-01
Incomplete spaces are investigated for solving the Schrödinger equation under the Born–Oppenheimer approximation. It is shown that the Hellmann–Feynman theorem cannot be used for computing the electronic force exerted on a nucleus, when a variational wavefunction with floating centers is used, if multicenter polynomial components are added in order to describe the polarization effects through the chemical bond. This is because the minimum of the potential energy surface is not a stationary point in the direction of the float parameter. Such a failure can be fixed by considering a molecular model with finite size nuclei, as defined herein. The classical electronic force is computed for that model, as compared with the standard point charge approximation, and it is applied to the H 2 + molecular ion. As a result, the former model is found more accurate by several orders of magnitude. (author)
On the coordinate (in)dependence of the formal path integral
DEFF Research Database (Denmark)
Johnson-Freyd, Theo
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path integral on the coordinates becomes much less obvious....... 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...
Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
Kleinert, Hagen
2009-01-01
This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p
Cross section evaluation by spinor integration: The massless case in 4D
International Nuclear Information System (INIS)
Feng Bo; Huang Rijun; Jia Yin; Luo Mingxing; Wang Honghui
2010-01-01
To get the total cross section of one interaction from its amplitude M, one needs to integrate |M| 2 over phase spaces of all outgoing particles. Starting from this paper, we will propose a new method to perform such integrations, which is inspired by the reduced phase space integration of one-loop unitarity cut developed in the last few years. The new method reduces one constrained three-dimension momentum space integration to a one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. The current paper is the first paper of a series for the new method. Here we have exclusively focused on massless particles in 4D. There is no need to carve out a complicated integration region in the phase space for this particular simple case because the integration region is always simply [0,1].
Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
Meyer, Christoph
2018-01-01
The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.
Alternative Evaluation of a ln tan Integral Arising in Quantum Field Theory
International Nuclear Information System (INIS)
Coffey, Mark W.
2010-01-01
A certain dilogarithmic integral I 7 turns up in a number of contexts including Feynman diagram calculations, volumes of tetrahedra in hyperbolic geometry, knot theory, and conjectured relations in analytic number theory. We provide an alternative explicit evaluation of a parameterized family of integrals containing this particular case. By invoking the Bloch-Wigner form of the dilogarithm function, we produce an equivalent result, giving a third evaluation of I 7 . We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl 2 .
Computer algebra in quantum field theory integration, summation and special functions
Schneider, Carsten
2013-01-01
The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including
Quantum mechanics 1. Path-integral formulation and operator formalism
International Nuclear Information System (INIS)
Reinhardt, Hugo
2012-01-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
International Nuclear Information System (INIS)
Kwato Njock, M.G.; Bona, Z.; Nsangou, M.; Nana Engo, S.G.; Oumarou, B.
1999-02-01
The hypervirial and Hellmann-Feynman theorems are used in the methods of 1/N expansion to construct Rayleigh-Schroedinger perturbation expansion for bound-state energy eigenvalues of spherical symmetric potentials. A new iteration procedure of calculating correction terms of arbitrarily high orders is obtained for any kind of 1/N expansion. The recurrence formulas for three variants of the 1/N expansion are considered in this work, namely, the 1/n expansion, the shifted and unshifted 1/N expansions which are applied to the Gaussian and Patil potentials. As a result, their credibility could be reliably judged when account is taken of high order terms of the eigenenergies. It is also found that there is a distinct advantage in using the shifted 1/N expansion over the two other versions. However, the shifted 1/N expansion diverges for s states and in certain cases is not applicable as far as complicated potentials are concerned. In an effort to solve these problems we have incorporated the principle of minimal sensitivity in the shifted 1/N expansion as a first step toward extending the scope of applicability of that technique, and then we have tested the obtained approach to some unfavorable cases of the Patil and Hellmann potentials. The agreement between our numerical calculations and reference data is quite satisfactory. (author)
Energy Technology Data Exchange (ETDEWEB)
Frabboni, Stefano [Department FIM, University of Modena and Reggio Emilia, Via G. Campi 213/a, 41125 Modena (Italy); CNR-Institute of Nanoscience-S3, Via G. Campi 213/a, 41125 Modena (Italy); Gazzadi, Gian Carlo [CNR-Institute of Nanoscience-S3, Via G. Campi 213/a, 41125 Modena (Italy); Grillo, Vincenzo [CNR-Institute of Nanoscience-S3, Via G. Campi 213/a, 41125 Modena (Italy); CNR-IMEM, Parco delle Scienze 37a, 43100 Parma (Italy); Pozzi, Giulio [Department of Physics and Astronomy, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy)
2015-07-15
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. - Highlights: • Fabrication by focused ion beam and electron beam induced deposition of two slits covered by electron transparent materials. • Two slits interference experiment with elastic and inelastic electrons. • Analysis of Fraunhofer and Fresnel images of the two slits formed with elastic and inelastic (plasmon loss) electrons.
Energy Technology Data Exchange (ETDEWEB)
Gabrielli, A. [Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Department of Physics, University of Bologna (Italy); Giorgi, F.M., E-mail: giorgi@bo.infn.it [Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Semprini, N.; Villa, M.; Zoccoli, A. [Istituto Nazionale di Fisica Nucleare, Bologna (Italy); Department of Physics, University of Bologna (Italy); Matteucci, G.; Pozzi, G. [Department of Physics, University of Bologna (Italy); Frabboni, S. [Department of Physics, University of Modena and Reggio Emilia (Italy); CNR-Institute of Nanoscience-S3, Modena (Italy); Gazzadi, G.C. [CNR-Institute of Nanoscience-S3, Modena (Italy)
2013-01-21
A monolithic CMOS detector, made of 4096 active pixels developed for HEP collider experiments, has been used in the Young–Feynman two-slit experiment with single electrons. The experiment has been carried out by inserting two nanometric slits in a transmission electron microscope that provided the electron beam source and the electro-optical lenses for projecting and focusing the interference pattern on the sensor. The fast readout of the sensor, in principle capable to manage up to 10{sup 6} frames per second, allowed to record single-electron frames spaced by several empty frames. In this way, for the first time in a single-electron two-slit experiment, the time distribution of electron arrivals has been measured with a resolution of 165μs. In addition, high statistics samples of single-electron events were collected within a time interval short enough to be compatible with the stability of the system and coherence conditions of the illumination.
Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Tarasov, Oleg V.
2009-04-01
The method for obtaining functional equations, recently proposed by one of the authors (O. V. Tarasov, 2008), is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation. (orig.)
Colored graphs and matrix integrals
International Nuclear Information System (INIS)
Artamkin, I.V.
2007-12-01
In this article we discuss two different asymptotic expansions of matrix integrals. The original approach using the so-called Feynman diagram techniques leads to sums over isomorphism classes of ribbon graphs. Asymptotic expansions of more general Gaussian integrals are sums over isomorphism classes of colored graphs without ribbon structure. Here we derive the former expansion from the latter one. This provides an independent proof for the expansion used by Kontsevich. It might be very interesting to compare the algebra arising in these two approaches. The asymptotic expansion using ribbon graphs leads to the tau function of the KDV hierarchy while the sums over colored graphs satisfy simple partial differential equations which generalize the Burgers equation. We describe the general approach using colored graphs in the second section. In the third section we specialize the results of the second section for the matrix integral. In this section we also derive the expansion over ribbon graphs. The proof is based on simple topological considerations which are contained in section 5. In the last section we give an explicit calculation of the first term of the expansion using colored graphs
Nonperturbative path integral expansion II
International Nuclear Information System (INIS)
Kaiser, H.J.
1976-05-01
The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)
Functional integral for non-Lagrangian systems
Kochan, Denis
2010-01-01
A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\\kappa[\\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
Pre-asymptotic behavior of single-particle overlap integrals of non-Borromean two-neutron halos
International Nuclear Information System (INIS)
Timofeyuk, N.K.; Tostevin, J.A.; Blokhintsev, L.D.
2003-01-01
For non-Borromean two-neutron halo nuclei, modifications to the behavior of single-particle overlap integrals will arise due to the correlations of the two interacting nucleons in the halo. An additional contribution to the overlap integral can be obtained using the Feynman diagram approach. This additional term is modeled using a simple local potential model. We show that these modifications may play a role in detailed interpretations of experimental results from single-nucleon knockout, transfer, and other reactions that probe the single-nucleon overlap functions
Channel Capacity Calculation at Large SNR and Small Dispersion within Path-Integral Approach
Reznichenko, A. V.; Terekhov, I. S.
2018-04-01
We consider the optical fiber channel modelled by the nonlinear Shrödinger equation with additive white Gaussian noise. Using Feynman path-integral approach for the model with small dispersion we find the first nonzero corrections to the conditional probability density function and the channel capacity estimations at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity in small dimensionless dispersion parameter is quadratic and positive therefore increasing the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region. Also for small dispersion case we find the analytical expressions for simple correlators of the output signals in our noisy channel.
Path integral quantization of gravitational interactions
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1985-07-01
Some of the local symmetry properties of quantum field theory in curved space-time and quantized gravitational interactions are discussed. We concentrate on local symmetry properties, and thus the asymptotically flat space-time is assumed, whenever necessary, in the hope that the precise boundary conditions will not modify the short distance structure in quantum theory. We adopt the DeWitt-Faddeev-Popov prescription of the Feynman path integral with a complete gauge fixing. The topics discussed include: (i) A brief review of the path integral derivation of chiral anomalies in flat space-time. (ii) The specification of the gravitational path integral measure, which avoids all the ''fake'' gravitational anomalies, and the applications of this path integral prescription to 1) effective potential in generalized Kaluza-Klein theory, 2) 4-dimensional conformal anomalies, 3) conformal symmetry in pure conformal gravity, 4) bosonic string theory as a gravitational theory in d = 2, 5) Virasoro condition and the Wheeler-DeWitt equation in the path integral formalism, 6) gravitational anomalies and the definition of the energy-momentum tensor. (author)
Microcanonical functional integral for the gravitational field
International Nuclear Information System (INIS)
Brown, J.D.; York, J.W. Jr.
1993-01-01
The gravitational field in a spatially finite region is described as a microcanonical system. The density of states ν is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by any real stationary axisymmetric black hole, then in this same approximation lnν is shown to equal 1/4 the area of the black-hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of ν that lead to ''imaginary-time'' functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function
The two-loop master integrals for qq-bar→VV
International Nuclear Information System (INIS)
Gehrmann, Thomas; Manteuffel, Andreas von; Tancredi, Lorenzo; Weihs, Erich
2014-01-01
We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, qq-bar→VV, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion
Integral equations of hadronic correlation functions a functional- bootstrap approach
Manesis, E K
1974-01-01
A reasonable 'microscopic' foundation of the Feynman hadron-liquid analogy is offered, based on a class of models for hadron production. In an external field formalism, the equivalence (complementarity) of the exclusive and inclusive descriptions of hadronic reactions is specifically expressed in a functional-bootstrap form, and integral equations between inclusive and exclusive correlation functions are derived. Using the latest CERN-ISR data on the two-pion inclusive correlation function, and assuming rapidity translational invariance for the exclusive one, the simplest integral equation is solved in the 'central region' and an exclusive correlation length in rapidity predicted. An explanation is also offered for the unexpected similarity observed between pi /sup +/ pi /sup -/ and pi /sup -/ pi /sup -/ inclusive correlations. (31 refs).
Virial expansion with Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Leyronas, X. [Laboratoire de Physique Statistique, Ecole Normale Superieure, UPMC Universite Paris 06, Universite Paris Diderot, CNRS, 24 rue Lhomond, FR-75005 Paris (France)
2011-11-15
We present a field theoretic method for the calculation of the second and third virial coefficients b{sub 2} and b{sub 3} of two-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b{sub 3} in terms of the two- and three-body T matrices. We recover numerically, at unitarity, and also in the whole Bose-Einstein-condensate-BCS crossover, previous numerical results for the third virial coefficient b{sub 3}.
Integrability of conformal fishnet theory
Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory; Negro, Stefano; Sizov, Grigory
2018-01-01
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R-matrix of non-compact conformal SU(2 , 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q-functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr( ϕ 1 J ) where ϕ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2 , 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2009-11-01
Full Text Available The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.
'String amplitudes': What can we do about the divergent integrals?
International Nuclear Information System (INIS)
Amano, Kaoru
1990-01-01
The rules for perturbative construction of scattering amplitude constitute the most well-established part of the string theory. They lead to neat integral expressions that represent the amplitude as the sum over the geometry of the string world sheet. However, if one really tries to evaluate the expression, one has to go a long way from there, for the integral does not represent the amplitude in any direct way. The present report focuses on this problem. A study is made to show that the traditional integrals purporting to be string amplitudes are divergent and to identify a remedy. Obviously, any divergent amplitude is not acceptable in a case like the one-loop four-point amplitude. Although the origin of the divergences seems to relate to physical singularities, the integral fails to give imaginary part required for unitarity but only gives infinities which are not desired. Respecting the observation that the integral representation corresponds to the Euclidean Feynman integral, one may modify the integral by postulating an offshell integral for a certain Euclidean, then continuing the function analytically, and defining the physical amplitude by the limit value of the function. This would take one to the correct Minkowskian expression. Some examples are also shown. (N.K.)
Leading singularities and off-shell conformal integrals
Energy Technology Data Exchange (ETDEWEB)
Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.
2013-08-29
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.
α′-Expansion of open string disk integrals via Mellin transformations
Directory of Open Access Journals (Sweden)
Ellis Ye Yuan
2015-02-01
Full Text Available Open string disk integrals are represented as contour integrals of a product of Beta functions using Mellin transformations. This makes the mathematical problem of computing the α′-expansion around the field-theory limit similar to that of the ϵ-expansion in Feynman loop integrals around the four-dimensional limit. More explicitly, the formula in Mellin space obtained directly from the standard Koba–Nielsen-like representation is valid in a region of values of α′ that does not include α′=0. Analytic continuation is therefore needed since contours are pinched by poles as α′→0. Deforming contours that get pinched by poles generates a set of (n−3! multi-dimensional residues left behind which contain all the field theory information. Some analogies between the field theory formulas obtained by this method and those derived recently from using the scattering equations are commented at the end.
Ray optics for diffraction: a useful paradox in a path integral context
International Nuclear Information System (INIS)
Schulman, L.S.
1984-01-01
Geometrical diffraction theory uses ray tracing techniques to calculate diffraction and other properties of the electromagnetic field generally considered characteristically wave like. The author studies this dualism of the classical electromagnetic field so as to distinguish those aspects of quantum dualism that arise simply as properties of oscillatory integrals and those that may have deeper origins. By a series of transformations the solutions of certain optics problems are reduced to the evaluation of a Feynman path integral and the known semiclassical approximations for the path integral provide a justification for the geometrical diffraction theory. Particular attention is paid to the problem of edge diffraction and for a half plane barrier a closed form solution is obtained. A classical variational principle for barrier penetration is also presented. (Auth.)
Integral or integrated marketing
Directory of Open Access Journals (Sweden)
Davčik Nebojša
2006-01-01
Full Text Available Marketing theorists and experts try to develop business efficient organization and to get marketing performance at higher, business integrated level since its earliest beginnings. The core issue in this paperwork is the dialectic and practical approach dilemma should we develop integrated or integral marketing approach in the organization. The presented company cases as well as dialectic and functional explanations of this dilemma clearly shows that integrated marketing is narrower approach than integral marketing if we take as focal point new, unique and completed entity. In the integration the essence is in getting different parts together, which do not have to make necessary the new entity. The key elements in the definition of the integral marketing are necessity and holistic, e.g. necessity to develop new, holistic entity.
Milton, Kimball A
2015-01-01
Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.
Energy Technology Data Exchange (ETDEWEB)
Frabboni, Stefano [Department of Physics, University of Modena and Reggio Emilia, Via G. Campi 213/a, 41125 Modena (Italy); CNR-Institute of Nanoscience-S3, Via G. Campi 213/a, 41125 Modena (Italy); Gabrielli, Alessandro [Department of Physics, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy); INFN, Viale B. Pichat 6/2, 40127 Bologna (Italy); Carlo Gazzadi, Gian [CNR-Institute of Nanoscience-S3, Via G. Campi 213/a, 41125 Modena (Italy); Giorgi, Filippo [Department of Physics, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy); INFN, Viale B. Pichat 6/2, 40127 Bologna (Italy); Matteucci, Giorgio [Department of Physics, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy); Pozzi, Giulio, E-mail: giulio.pozzi@unibo.it [Department of Physics, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy); Cesari, Nicola Semprini; Villa, Mauro; Zoccoli, Antonio [Department of Physics, University of Bologna, Viale B. Pichat 6/2, 40127 Bologna (Italy); INFN, Viale B. Pichat 6/2, 40127 Bologna (Italy)
2012-05-15
The two-slits experiment for single electrons has been carried out by inserting in a conventional transmission electron microscope a thick sample with two nano-slits fabricated by Focused Ion Beam technique and a fast recording system able to measure the electron arrival-time. The detector, designed for experiments in future colliders, is based on a custom CMOS chip equipped with a fast readout chain able to manage up to 10{sup 6} frames per second. In this way, high statistic samples of single electron events can be collected within a time interval short enough to measure the distribution of the electron arrival-times and to observe the build-up of the interference pattern. -- Highlights: Black-Right-Pointing-Pointer We present the first results obtained regarding the two-slits Young-Feynman experiment with single electrons. Black-Right-Pointing-Pointer We use two nano-slits fabricated by Focused Ion Beam technique. Black-Right-Pointing-Pointer We insert in the transmission electron microscope a detector, designed for experiments in future colliders. Black-Right-Pointing-Pointer We record the build-up of high statistic single electron interference patterns. Black-Right-Pointing-Pointer We measure the time distribution of electron arrivals.
Once-through integral system (OTIS): Final report
International Nuclear Information System (INIS)
Gloudemans, J.R.
1986-09-01
A scaled experimental facility, designated the once-through integral system (OTIS), was used to acquire post-small break loss-of-coolant accident (SBLOCA) data for benchmarking system codes. OTIS was also used to investigate the application of the Abnormal Transient Operating Guidelines (ATOG) used in the Babcock and Wilcox (B and W) designed nuclear steam supply system (NSSS) during the course of an SBLOCA. OTIS was a single-loop facility with a plant to model power scale factor of 1686. OTIS maintained the key elevations, approximate component volumes, and loop flow resistances, and simulated the major component phenomena of a B and W raised-loop nuclear plant. A test matrix consisting of 15 tests divided into four categories was performed. The largest group contained 10 tests and was defined to parametrically obtain an extensive set of plant-typical experimental data for code benchmarking. Parameters such as leak size, leak location, and high-pressure injection (HPI) shut-off head were individually varied. The remaining categories were specified to study the impact of the ATOGs (2 tests), to note the effect of guard heater operation on observed phenomena (2 tests), and to provide a data set for comparison with previous test experience (1 test). A summary of the test results and a detailed discussion of Test 220100 is presented. Test 220100 was the nominal or reference test for the parametric studies. This test was performed with a scaled 10-cm 2 leak located in the cold leg suction piping
Two-loop planar master integrals for Higgs →3 partons with full heavy-quark mass dependence
International Nuclear Information System (INIS)
Bonciani, Roberto; Duca, Vittorio Del; Frellesvig, Hjalte; Henn, Johannes M.; Moriello, Francesco; Smirnov, Vladimir A.
2016-01-01
We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs→3 partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogarithms and elementary functions up to transcendental weight four. Two integral sectors are expressed in terms of elliptic integrals. We show that by introducing a one-dimensional parametrization of the integrals the relevant second order differential equation can be readily solved, and the solution can be expressed to all orders of the dimensional regularization parameter in terms of iterated integrals over elliptic kernels. We express the result for the elliptic sectors in terms of two and three-fold iterated integrals, which we find suitable for numerical evaluations. This is the first time that four-point multiscale Feynman integrals have been computed in a fully analytic way in terms of elliptic integrals.
CSIR Research Space (South Africa)
Ackermann, ER
2012-09-01
Full Text Available We use Cavalieri’s principle to develop a novel integration technique which we call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way we can use single Cavalieri...
Improving the variational path integral approach to the quantum double-well potential
International Nuclear Information System (INIS)
Bao Jingdong; Wang Hongyu
2002-01-01
An improved variational path integral approach is developed and applied to the quantum double-well potential, in which part of the quartic term of the potential is included in the trial action. The expression of the effective classical potential (ECP) under a non-Gaussian expectation is obtained. Here the frequency and fourth-order derivative of the potential are treated as two variational parameters, determined by the minimization of the ECP at each point. We calculate the ECP, the free energy and the level splitting of a symmetrical double-well potential. It is shown that the present results are better than those of the Feynman-Kleinert Gaussian variational method. (author)
Path Integrals and Anomalies in Curved Space
Energy Technology Data Exchange (ETDEWEB)
Louko, Jorma [University of Nottingham (United Kingdom)
2007-04-07
Bastianelli and van Nieuwenhuizen's monograph 'Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaume and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will
An Intrinsic Fiber-Optic Single Loop Micro-Displacement Sensor
Directory of Open Access Journals (Sweden)
Guillermo Salceda-Delgado
2012-01-01
Full Text Available A micro-displacement sensor consisting of a fiber-loop made with a tapered fiber is reported. The sensor operation is based on the interaction between the fundamental cladding mode propagating through the taper waist and higher order cladding modes excited when the taper is deformed to form a loop. As a result, a transmission spectrum with several notches is observed, where the notch wavelength resonances shift as a function of the loop diameter. The loop diameter is varied by the spatial displacement of one end of the fiber-loop attached to a linear translation stage. In a displacement range of 3.125 mm the maximum wavelength shift is 360.93 nm, with 0.116 nm/μm sensitivity. By using a 1,280 nm broadband low-power LED source and a single Ge-photodetector in a power transmission sensor setup, a sensitivity in the order of 2.7 nW/μm is obtained in ~1 mm range. The proposed sensor is easy to implement and has a plenty of room to improve its performance.
A single loop is essential for the octamerization of vanillyl alcohol oxidase
Ewing, Tom A.; Gygli, Gudrun; Berkel, van Willem J.H.
2016-01-01
The VAO/PCMH family of flavoenzymes is a family of structurally related proteins that catalyse a wide range of oxidation reactions. It contains a subfamily of enzymes that catalyse the oxidation of para-substituted phenols using covalently bound FAD cofactors (the 4PO subfamily). This subfamily
In vivo heating pattern of an implantable single loop applicator measured at S-band
International Nuclear Information System (INIS)
Feldman, A.; Roelofs, T.; Weaver, P.; Maturan, A.
1984-01-01
The authors have measured the temperatures achieved by an implantable applicator buried in both normal and tumor tissue. The temperature distribution correlated with that measured in phantom material; high temperatures were achieved at the center of the coil, lower temperatures near the edges but within the coil, and much lower temperatures outside the coil. Sheathed in PTFE teflon the coil is compatible with tissue for long-term implantation. This device appeared well-suited for long-term invasive hyperthermia since it delivered a heat dose to a specific tumor volume while sparing the surrounding normal tissue and was found to be biocompatible with normal tissue
Integral trees and integral graphs
Wang, Ligong
2005-01-01
This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.
Path Integrals and Anomalies in Curved Space
International Nuclear Information System (INIS)
Louko, Jorma
2007-01-01
Bastianelli and van Nieuwenhuizen's monograph 'Path Integrals and Anomalies in Curved Space' collects in one volume the results of the authors' 15-year research programme on anomalies that arise in Feynman diagrams of quantum field theories on curved manifolds. The programme was spurred by the path-integral techniques introduced in Alvarez-Gaume and Witten's renowned 1983 paper on gravitational anomalies which, together with the anomaly cancellation paper by Green and Schwarz, led to the string theory explosion of the 1980s. The authors have produced a tour de force, giving a comprehensive and pedagogical exposition of material that is central to current research. The first part of the book develops from scratch a formalism for defining and evaluating quantum mechanical path integrals in nonlinear sigma models, using time slicing regularization, mode regularization and dimensional regularization. The second part applies this formalism to quantum fields of spin 0, 1/2, 1 and 3/2 and to self-dual antisymmetric tensor fields. The book concludes with a discussion of gravitational anomalies in 10-dimensional supergravities, for both classical and exceptional gauge groups. The target audience is researchers and graduate students in curved spacetime quantum field theory and string theory, and the aims, style and pedagogical level have been chosen with this audience in mind. Path integrals are treated as calculational tools, and the notation and terminology are throughout tailored to calculational convenience, rather than to mathematical rigour. The style is closer to that of an exceedingly thorough and self-contained review article than to that of a textbook. As the authors mention, the first part of the book can be used as an introduction to path integrals in quantum mechanics, although in a classroom setting perhaps more likely as supplementary reading than a primary class text. Readers outside the core audience, including this reviewer, will gain from the book a
Polymer density functional approach to efficient evaluation of path integrals
DEFF Research Database (Denmark)
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures....... The exact solution is not, though, reachable in three dimensions (3D) because of a vast amount of storage required for 2p-PCF. In order to treat closed paths in 3D, we introduce a so-called "open ring" approximation which proves to be rather accurate in the limit of long chains. We also employ a simple self...
Energy Technology Data Exchange (ETDEWEB)
Karbstein, Felix
2009-07-08
We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''{pi} meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko; Li, J.; Pap, E.
2015-01-01
Roč. 259, č. 1 (2015), s. 3-11 ISSN 0165-0114 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Choquet integral * Decomposition integral * Superdecomposition integral * Convex integral Subject RIV: BA - General Mathematics Impact factor: 2.098, year: 2015 http://library.utia.cas.cz/separaty/2015/E/mesiar-0442006.pdf
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 11. Riemann Integration. Dilip P Patil. General Article Volume 11 Issue 11 November 2006 pp 61-80 ... Keywords. Area; lower and upper sums; Riemann sums; integrable functions; definite integral; derivative; primitive; anti-derivative.
Thomas, E. G. F.
2012-01-01
This paper deals with the theory of integration of scalar functions with respect to a measure with values in a, not necessarily locally convex, topological vector space. It focuses on the extension of such integrals from bounded measurable functions to the class of integrable functions, proving
Errors in The Feynman Lectures on Physics
Indian Academy of Sciences (India)
IAS Admin
GENERAL ARTICLE. RESONANCE. May 2016. 4. ERROR 2: Bilateral Symmetry vs. Two-Fold Axis. The following quote is from FLP, Vol 1, Section 11-1: “The word “symmetry” is used here with a special mean- ing, and therefore needs to be defined. When a thing is symmetrical-how can we define it? When we have a pic-.
Errors in The Feynman Lectures on Physics
Indian Academy of Sciences (India)
Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 3. Current Issue Volume 23 | Issue 3. March 2018. Home · Volumes & Issues · Categories · Special Issues · Search · Editorial Board · Information for Authors · Subscription ...
Improved Figure of Merit for Feynman Histograms
Energy Technology Data Exchange (ETDEWEB)
Arthur, Jennifer Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-10-06
Typically a FOM that takes into account the differences between each bin of the histograms, as compared to the magnitude of the combination of the corresponding uncertainties, is used. Because the uncertainties corresponding to the larger multiplet bins are inherently larger than those of the smaller multiplet bins, this type of FOM puts more weight on differences between smaller multiplet bins. New proposed FOM also takes into account sensitivity of leakage multiplication (which is most sensitive to higher multiplet bins) to each bin in the histogram.
Errors in The Feynman Lectures on Physics
Indian Academy of Sciences (India)
IAS Admin
gives what to repeat. A lattice is a geometrical scaffolding to which atoms are attached to get the physical crystal. The fact that crystals are 3D periodic arrangements of atoms can also be expressed by stating that they have 3D translational. Rajesh Prasad teaches materials science at the. Indian Institute of. Technology Delhi ...
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hugo [Tuebingen Univ. (Germany). Inst. fuer Theoretische Physik
2012-11-01
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Interorganisational Integration
DEFF Research Database (Denmark)
Lyngsø, Anne Marie; Godtfredsen, Nina Skavlan; Frølich, Anne
2016-01-01
INTRODUCTION: Despite many initiatives to improve coordination of patient pathways and intersectoral cooperation, Danish health care is still fragmented, lacking intra- and interorganisational integration. This study explores barriers to and facilitators of interorganisational integration...... at a university hospital in the Capital Region of Denmark. RESULTS AND DISCUSSION: Our results can be grouped into five influencing areas for interorganisational integration: communication/information transfer, committed leadership, patient engagement, the role and competencies of the general practitioner...... and organisational culture. Proposed solutions to barriers in each area hold the potential to improve care integration as experienced by individuals responsible for supporting and facilitating it. Barriers and facilitators to integrating care relate to clinical, professional, functional and normative integration...
Rainey, Larry; Miller, Roxanne Greitz
1997-01-01
Describes the Integrated Science program that integrates biology, earth/space science, chemistry, and physics over a three-year, spiraling sequence arranged around broad themes such as cycles, changes, patterns, and waves. Includes weekly telecasts via public television and satellite, teacher manuals, student handbooks, e-mail connections, staff…
DEFF Research Database (Denmark)
Lenau, Torben Anker
1999-01-01
A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)......A homepage on the internet with course material, lecture plan, student exercises, etc. Continuesly updated during the course Integrated Design (80402, 80403)...
Bauböck, Rainer
1995-01-01
from the Table of Contents: Migration and integration - Basic concepts and definitions; Immigration and Integration policies; The legal framework for integration; Dimension of social integration; Cultural integration; Conclusions;
Integration of Chandrasekhar's integral equation
International Nuclear Information System (INIS)
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
International Nuclear Information System (INIS)
Menskii, M.B.
1993-01-01
Any real physical process takes place in an external (with respect to the investigated system) medium whose state reflects information about the behavior of the system. Therefore, a real model of any process must include a description of the measurement process. This has the consequence that the dynamics of a real system contains both quantum and classical elements. Mathematically, a quantum system subject to continuous measurement can be described by a restricted path integral. The Feynman path integral that is usually employed is an idealization that is not correct in all cases. In a real situation in which the path integral is restricted, the difficulties associated with the mathematical definition of the path integral disappear. These difficulties are a consequence of an unphysical idealization - the neglect of the fact that some information about the behavior of the quantum system remains in classical form in the environment. The aim of this paper is to show that the well-known difficulties in the mathematically rigorous definition of path integrals disappear if allowance is made for the specific interaction of a quantum system with its environment in which information about the state of the system is extracted. The consequences are evaluated of establishing the changes resulting from giving up the ideal model of an isolated system and accepting that some information about the behavior of the system remains outside it in classical form. 16 refs
Golinko, I. M.; Kovrigo, Yu. M.; Kubrak, A. I.
2014-03-01
An express method for optimally tuning analog PI and PID controllers is considered. An integral quality criterion with minimizing the control output is proposed for optimizing control systems. The suggested criterion differs from existing ones in that the control output applied to the technological process is taken into account in a correct manner, due to which it becomes possible to maximally reduce the expenditure of material and/or energy resources in performing control of industrial equipment sets. With control organized in such manner, smaller wear and longer service life of control devices are achieved. A unimodal nature of the proposed criterion for optimally tuning a controller is numerically demonstrated using the methods of optimization theory. A functional interrelation between the optimal controller parameters and dynamic properties of a controlled plant is numerically determined for a single-loop control system. The results obtained from simulation of transients in a control system carried out using the proposed and existing functional dependences are compared with each other. The proposed calculation formulas differ from the existing ones by a simple structure and highly accurate search for the optimal controller tuning parameters. The obtained calculation formulas are recommended for being used by specialists in automation for design and optimization of control systems.
International Nuclear Information System (INIS)
Krasnokutskij, R.N.; Kurchaninov, L.L.; Fedyakin, N.N.; Shuvalov, R.S.
1989-01-01
Two measuring techniques for signal amplitude of particle detector without the in-side amplification: with peak detector and with strobed integrator are compared. Simple formulae to calculate noise value at the output of strobed integrator are derived. Usage of strobed integrator is shown to enable to increase essentially counting rate as compared to peak detector at the same noise level. Optimal positioning strobe-pulse with regard to the input signal is determined. Equivalent noise charge ar signal shaping sifferent schemes is calculated
McKean, Henry P
2005-01-01
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen
Rosen, Charles; Siegel, Edward Carl-Ludwig; Feynman, Richard; Wunderman, Irwin; Smith, Adolph; Marinov, Vesco; Goldman, Jacob; Brine, Sergey; Poge, Larry; Schmidt, Erich; Young, Frederic; Goates-Bulmer, William-Steven; Lewis-Tsurakov-Altshuler, Thomas-Valerie-Genot; Ibm/Exxon Collaboration; Google/Uw Collaboration; Microsoft/Amazon Collaboration; Oracle/Sun Collaboration; Ostp/Dod/Dia/Nsa/W.-F./Boa/Ubs/Ub Collaboration
2013-03-01
Belew[Finding Out About, Cambridge(2000)] and separately full-decade pre-Page/Brin/Google FIRST Siegel-Rosen(Machine-Intelligence/Atherton)-Feynman-Smith-Marinov(Guzik Enterprises/Exxon-Enterprises/A.-I./Santa Clara)-Wunderman(H.-P.) [IBM Conf. on Computers and Mathematics, Stanford(1986); APS Mtgs.(1980s): Palo Alto/Santa Clara/San Francisco/...(1980s) MRS Spring-Mtgs.(1980s): Palo Alto/San Jose/San Francisco/...(1980-1992) FIRST quantum-computing via Bose-Einstein quantum-statistics(BEQS) Bose-Einstein CONDENSATION (BEC) in artificial-intelligence(A-I) artificial neural-networks(A-N-N) and biological neural-networks(B-N-N) and Siegel[J. Noncrystalline-Solids 40, 453(1980); Symp. on Fractals..., MRS Fall-Mtg., Boston(1989)-5-papers; Symp. on Scaling..., (1990); Symp. on Transport in Geometric-Constraint (1990)
International Nuclear Information System (INIS)
Jekowski, J.; Aeby, I.
1979-01-01
The purpose of the R and D effort is to establish a baseline technology in integrated optic techniques within the EMG. Significant investment presently being made by industry in this area indicates that this technology may offer an alternative solution for high speed digital data acquisition and transmission. The objectives of this year's integrated optics program were three-fold: (1) to establish a literature search and maintain industry contacts in an attempt to make the needs of the Weapons Test Program known; (2) to assist the Las Vegas Hybrid facility in establising integrated optic fabrication techniques for their new Thin Film Laboratory; and (3) to conduct basic experiments at Los Alamos in the construction of photolithograhicaly etched plastic film devices. The report describes the successful completion of preliminary investigations into photolithographic techniques and continuing investigations into newly announced integrated optic techniques and devices that would be applicable to the weapons test program
DEFF Research Database (Denmark)
Knudsen, Lars Ramkilde; Wagner, David
2002-01-01
This paper considers a cryptanalytic approach called integral cryptanalysis. It can be seen as a dual to differential cryptanalysis and applies to ciphers not vulnerable to differential attacks. The method is particularly applicable to block ciphers which use bijective components only.......This paper considers a cryptanalytic approach called integral cryptanalysis. It can be seen as a dual to differential cryptanalysis and applies to ciphers not vulnerable to differential attacks. The method is particularly applicable to block ciphers which use bijective components only....
Path integral Monte Carlo and the electron gas
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational
Integrable spin chain in superconformal Chern-Simons theory
International Nuclear Information System (INIS)
Bak, Dongsu; Rey, Soo-Jong
2008-01-01
N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS 4 x CP 3 . We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong 't Hooft coupling, the spectrum is obtained from excitation energy of free superstring on OSp(6|4; R)/SO(3, 1) x SU(3) x U(1) supercoset. We recall that the worldsheet theory is integrable classically by utilizing well-known results concerning sigma model on symmetric space. With R-symmetry group SU(4), we also solve relevant Yang-Baxter equation for a spin chain system associated with the single trace operators. From the solution, we construct alternating spin chain Hamiltonian involving three-site interactions between 4 and 4-bar . At weak 't Hooft coupling, we study gauge theory perturbatively, and calculate action of dilatation operator to single trace operators up to two loops. To ensure consistency, we computed all relevant Feynman diagrams contributing to the dilatation opeator. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation. We further study new issues arising from the shortest gauge invariant operators TrY I Y † J = (15, 1). We observe that 'wrapping interactions' are present, compute the true spectrum and find that the spectrum agrees with prediction from supersymmetry. We also find that scaling dimension computed naively from alternating spin chain Hamiltonian coincides with the true spectrum. We solve Bethe ansatz equations for small number of excitations, and find indications of correlation between excitations of 4's and 4-bar 's and of nonexistence of mesonic (44-bar ) bound-state.
DEFF Research Database (Denmark)
Axelsson, Runo
2013-01-01
to large-scale bureaucratic structures of centralised control. In the 1980’s there was a period of decentralisation to smaller organisational units, which was followed in the 1990’s by an introduction of market mechanisms in accordance with the New Public Management. During this period, there has been......Background: In Sweden, as in many other countries, there has been a succession of trends in the organisation of health care and other welfare services. These trends have had different implications for the integration of services in the health and welfare system. Aims: One aim is to discuss...... the implications of different organisational trends for the integration of health and welfare services. Another aim is to introduce a Swedish model of financial coordination as a flexible way to organise integration. Organisational trends: In the 1960’s there was an expansion of health and welfare services leading...
Williamson, JH
2014-01-01
This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult. The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, co
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
Sinitskiy, Anton V; Voth, Gregory A
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
DEFF Research Database (Denmark)
Jørgensen, Michael; Nielsen, M. W.; Strømann-Andersen, Jakob Bjørn
2011-01-01
This paper presents a case study of the implementation of integrated design in an actual architectural competition. The design process was carried out at a highly esteemed architectural office and attended by both engineers and architects working towards mutual goals of architectural excellence......, low-energy consumption, and high-quality indoor environment. We use this case study to investigate how technical knowledge about building performance can be integrated into the conceptual design stage. We have selected certain points during the design process that represented design challenges......'s performance. This article illustrates how a continuous implementation of technical knowledge early in the design process for an actual architectural competition resulted in a building design with an energy demand approximately 30% lower than Danish building regulations, yet which still maintains a high...
DEFF Research Database (Denmark)
Petersson, Eva
2005-01-01
Toys play a crucial role in supporting children’s learning and creation of meaning in their everyday life. Children also play with toys out of an interest to interact with others e.g. peers and adults. Tendencies of digital technology in toys have led to greater opportunities for manipulation...... changed our everyday lives. However, its contribution in development of new suitable material for play and learning has not been appropriate. We argue that play is a fruitful base for learning and training and that the design of physical and virtual artifacts advantageously should rest upon...... and interaction with the integrated toy as a virtual experience without attachment or wearable on the body, which in context would not be appropriate. In the field of rehabilitation integrated toys are still at an embryonic stage and as such an under used resource for rehabilitation. Qualitative method...
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
DEFF Research Database (Denmark)
Merlo, Domenico Franco; Vahakangas, Kirsi; Knudsen, Lisbeth E.
2008-01-01
Environmental health research is a relatively new scientific area with much interdisciplinary collaboration. Regardless of which human population is included in field studies (e.g., general population, working population, children, elderly, vulnerable sub-groups, etc.) their conduct must guarantee...... consent was obtained.Integrity is central to environmental health research searching for causal relations. It requires open communication and trust and any violation (i.e., research misconduct, including fabrication or falsification of data, plagiarism, conflicting interests, etc.) may endanger...
Diagrammatical methods within the path integral representation for quantum systems
International Nuclear Information System (INIS)
Alastuey, A
2014-01-01
The path integral representation has been successfully applied to the study of equilibrium properties of quantum systems for a long time. In particular, such a representation allowed Ginibre to prove the convergence of the low-fugacity expansions for systems with short-range interactions. First, I will show that the crucial trick underlying Ginibre's proof is the introduction of an equivalent classical system made with loops. Within the Feynman-Kac formula for the density matrix, such loops naturally emerge by collecting together the paths followed by particles exchanged in a given cyclic permutation. Two loops interact via an average of two- body genuine interactions between particles belonging to different loops, while the interactions between particles inside a given loop are accounted for in a loop fugacity. It turns out that the grand-partition function of the genuine quantum system exactly reduces to its classical counterpart for the gas of loops. The corresponding so-called magic formula can be combined with standard Mayer diagrammatics for the classical gas of loops. This provides low-density representations for the quantum correlations or thermodynamical functions, which are quite useful when collective effects must be taken into account properly. Indeed, resummations and or reorganizations of Mayer graphs can be performed by exploiting their remarkable topological and combinatorial properties, while statistical weights and bonds are purely c-numbers. The interest of that method will be illustrated through a brief description of its application to two long-standing problems, namely recombination in Coulomb systems and condensation in the interacting Bose gas.
Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E
2018-03-14
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.
2018-03-01
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
Czech Academy of Sciences Publication Activity Database
Ryska, O.; Martinek, J.; Filípková, T.; Doležel, R.; Juhásová, Jana; Motlík, Jan; Zavoral, M.; Ryska, M.
2012-01-01
Roč. 7, č. 4 (2012), s. 233-239 ISSN 1895-4588 R&D Projects: GA MZd NS9994 Institutional research plan: CEZ:AV0Z50450515 Keywords : natural orifice transluminal endoscopic surgery * gastric closure * clips * endoloop Subject RIV: FJ - Surgery incl. Transplants Impact factor: 0.757, year: 2012
Directory of Open Access Journals (Sweden)
Bin Ai
2017-03-01
Full Text Available In this study, the first author narrates his experiences of the challenges of integration into several Chinese universities as a PhD graduate after returning from Australia. His patterns of communication and psychological changes are examined in terms of identity construction and transformation. His insider position as a Chinese native and academic returnee enables him to see the realities of practice in average Chinese universities at close range, yet with the altered vision gained from his overseas experience. This study highlights the challenges for academic returnees in Chinese higher education institutions and may also have resonances for academic returnees in other countries. Wider questions about the assessment of English research writing and the attitudes to academic returnees in Chinese universities are raised, contributing to debate over the future development of Chinese higher education institutions in a globalizing world.
Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom
Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.
2017-01-01
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.
Numerical Contour Integration for Loop Integrals
Kurihara, Y.; Kaneko, T.
2005-01-01
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and efficient numerical integrations an along appropriate contour can be performed for tensor integrals as well as for scalar ones appearing in loop calculations of the standard model. Examples of 3- and 4-point diagrams in 1-loop integrals and 2- and 3-point ...
Definite Integrals using Orthogonality and Integral Transforms
Directory of Open Access Journals (Sweden)
Howard S. Cohl
2012-10-01
Full Text Available We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
Sesquilinear uniform vector integral
Indian Academy of Sciences (India)
absolute integral which generalizes the Lebesgue integral and is more easy to manipulate. We speak so far about scalar integrals (scalar functions integrated with respect to positive measures-speaking approximately). The idea of integrating vector functions with respect to scalar measures came naturally on the scene of ...
Directory of Open Access Journals (Sweden)
Maria de Los Angeles Fanaro
2016-09-01
Full Text Available http://dx.doi.org/10.5007/2175-7941.2016v33n2p477 En este trabajo se presenta un conjunto de situaciones que componen una secuencia diseñada para enseñar conceptos relativos a la luz, que incluyen y enfatizan su aspecto cuántico, con el fin de promover su conceptualización en estudiantes del último año de la escuela secundaria. La descripción y el análisis didáctico de las situaciones se realizan utilizando la Teoría de los Campos Conceptuales de Vergnaud, anticipando los posibles invariantes operatorios que los estudiantes utilizarán al afrontar las situaciones. Las situaciones se presentan en un marco conceptual unificador basado en el enfoque de Caminos Múltiples de Feynman para la mecánica cuántica. Se parte de un conjunto de experiencias relativas a la luz (en su mayoría realizables en el aula de clases para luego formular una explicación cuántica de las mismas. Este abordaje ofrece una vía posible para que los estudiantes de la escuela secundaria construyan el sentido de los conceptos cuánticos: caminos alternativos, camino de tiempo mínimo y distribución de probabilidad en la Experiencia de la Doble Rendija. Se realizan consideraciones didácticas basadas en la Teoría de los Campos Conceptuales.
Wealth Through Integration: Regional Integration and Poverty ...
International Development Research Centre (IDRC) Digital Library (Canada)
Wealth Through Integration: Regional Integration and Poverty-Reduction Strategies in West Africa. Book cover Wealth Through Integration. Directeur(s) : Elias T. Ayuk and Samuel T. Kaboré. Maison(s) d'édition : Springer, IDRC. 27 février 2013. ISBN : 9781461444145. 297 pages. e-ISBN : 9781552505441. Téléchargez le ...
Simplification of integrity constraints for data integration
DEFF Research Database (Denmark)
Christiansen, Henning; Martinenghi, Davide
2004-01-01
When two or more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. Efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be trusted......, because either the global database is known to be consistent or suitable actions have been taken to provide consistent views. The present work generalizes simplification techniques for integrity checking in traditional databases to the combined case. Knowledge of local consistency is employed, perhaps...... together with given a priori constraints on the combination, so that only a minimal number of tuples needs to be considered. Combination from scratch, integration of a new source, and absorption of local updates are dealt with for both the local-as-view and global-as-view approaches to data integration....
Tactical Systems Integration Laboratory
Federal Laboratory Consortium — The Tactical Systems Integration Laboratory is used to design and integrate computer hardware and software and related electronic subsystems for tactical vehicles....
Lui, M; Chan, Andy; Long, Josh
2011-01-01
Pro Spring Integration is an authoritative book from the experts that guides you through the vast world of enterprise application integration (EAI) and application of the Spring Integration framework towards solving integration problems. The book is:. * An introduction to the concepts of enterprise application integration * A reference on building event-driven applications using Spring Integration * A guide to solving common integration problems using Spring Integration What makes this book unique is its coverage of contemporary technologies and real-world information, with a focus on common p
Černiavskaitė, Marija
2017-01-01
This Bachelor's thesis presents SAP CRM and integration systems testing analysis: investigation in SAP CRM and SAP PO systems, presentation of relationship between systems, introduction to third-party system (non-SAP) – Network Informational System (NIS) which has integration with SAP, presentation of best CRM testing practises, analysis and recommendation of integration testing. Practical integration testing is done in accordance to recommendations.
Probabilistic Data Integration
van Keulen, Maurice
2017-01-01
Probabilistic data integration is a specific kind of data integration where integration problems such as inconsistency and uncertainty are handled by means of a probabilistic data representation. The approach is based on the view that data quality problems (as they occur in an integration process)
Energy Technology Data Exchange (ETDEWEB)
Grosche, C. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Pogosyan, G.S. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics]|[Guadalajara Univ., Jalisco (Mexico). Dept. de Matematicas CUCEI; Sissakian, A.N. [Joint Inst. of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics
2006-07-15
In this paper the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of non-constant curvature: these spaces are Darboux spaces D{sub I} and D{sub II}, respectively. On D{sub I} there are three and on D{sub II} foru such potentials, respectively. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D{sub I} in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (Constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge. (Orig.)
How integrated are immigrants?
Directory of Open Access Journals (Sweden)
Rickard Sandell
2015-12-01
Full Text Available Background: The successful integration of immigrants is seen as a principal means to secure economic growth and welfare in many countries. Success in this task depends on the capacity to formulate effective integration policies, which in turn is based on research capable of describing and explaining the integration process properly. Objective: Our objective is to define a conceptual and quantifiable measure of full immigrant integration.This enables a quantitative evaluation of how integrated immigrants are in a specific context in an immigrant - native system - a question poorly addressed by past research. Methods: Our approach consists of looking at the functional dependency of different integrationquantifiers on immigrant density. The empirical analysis uses register data from Spain. We focus on social integration and labour market integration in formal employment. Results: In our empirical analysis we find dramatic differences in immigrant integration levels across integration contexts. While labour market integration approaches the level of full integration, social integration quickly declines as immigration levels surge. It is shown that these differences are primarily due to the presence of social network effects in the social integration process, absent in the labour market integration process. Conclusions: Proper identification of integration deficits and its causes is likely to improve the efficiency of integration policy making, and the capacity to reach integration targets. Our framework has this quality. The research presented here shows that full labour market integration of immigrants is a realistic target. However, it also shows that, if left unattended, the segregation forces contained in social networks, quite dramatically obstruct the social integration process. Lack of social integration undermines the strategy of reliance on increasing immigration to secure future economic well-being that many governments andinternational
Buried waste integrated demonstration technology integration process
International Nuclear Information System (INIS)
Ferguson, J.S.; Ferguson, J.E.
1992-04-01
A Technology integration Process was developed for the Idaho National Energy Laboratories (INEL) Buried Waste Integrated Demonstration (BWID) Program to facilitate the transfer of technology and knowledge from industry, universities, and other Federal agencies into the BWID; to successfully transfer demonstrated technology and knowledge from the BWID to industry, universities, and other Federal agencies; and to share demonstrated technologies and knowledge between Integrated Demonstrations and other Department of Energy (DOE) spread throughout the DOE Complex. This document also details specific methods and tools for integrating and transferring technologies into or out of the BWID program. The document provides background on the BWID program and technology development needs, demonstrates the direction of technology transfer, illustrates current processes for this transfer, and lists points of contact for prospective participants in the BWID technology transfer efforts. The Technology Integration Process was prepared to ensure compliance with the requirements of DOE's Office of Technology Development (OTD)
Cavalieri Integration - CSIR Technical report
CSIR Research Space (South Africa)
Grobler, TL
2011-10-01
Full Text Available The authors use Cavalieri's principle to develop a novel integration technique which they call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way they can use...
Communicating European Integration – Information vs. Integration?
Directory of Open Access Journals (Sweden)
Alexander Reinfeldt
2014-02-01
Full Text Available This article deals with the apparent contradiction between elite-driven supranational European integration and public information efforts by supranational political actors from the early 1950s. Supranational European integration relied on rational governance by independent experts which provoked a structural democratic deficit. Until the early 1970s public participation had never been the main preoccupation of supranational political actors who instead considered the ‘permissive consensus’ to be a precondition for progress towards further European integration. And yet, from the very beginning European supranational political actors pursued information policies. At first, the article reconsiders the rationale of supranational European integration and outlines the basic features of supranational information policies. Then, the article empirically analyses the purposes that guided supranational political actors like the High Authority of the European Coal and Steel Community (ECSC and the Commissions of the European Economic Community (EEC and the European Atomic Community (EURATOM in pursuing information policies at all by discussing two significant examples: the EC information efforts directed at young audiences and the participation of the EC in fairs and exhibitions. It is argued that information policies were only in part pursued to communicate European integration to the public or to influence public opinion on European integration issues. In fact, the main intention and impact of supranational information efforts was to foster transnational European integration and co-operation, for example between member state governments and administrations, non-governmental actors or associations.
The Integrated Renovation Process
DEFF Research Database (Denmark)
Galiotto, Nicolas; Heiselberg, Per; Knudstrup, Mary-Ann
The Integrated Renovation Process (IRP) is a user customized methodology based on judiciously selected constructivist and interactive multi-criteria decision making methods (Galiotto, Heiselberg, & Knudstrup, 2014 (expected)). When applied for home renovation, the Integrated Renovation Process...
Semantic Integration Technonolgies Survey
Kalfoglou, Yannis; Hu, Bo; Reynolds, Dave; Shadbolt, Nigel
2005-01-01
The \\underline{University of Southampton} and \\underline{Hewlett Packard Laboratories at Bristol} are collaborating in a joint project, CROSI, to investigate semantic integration. \\textbf{CROSI}, which stands for Capturing, Representing, and Operationalising Semantic Integration, aims to advance the state-of-the-art for semantic integration technologies. Semantic integration has become a much debated topic in today's research agenda, especially with the advent of the Semantic Web. Its roots, ...
Integrated optics technology study
Chen, B.
1982-01-01
The materials and processes available for the fabrication of single mode integrated electrooptical components are described. Issues included in the study are: (1) host material and orientation, (2) waveguide formation, (3) optical loss mechanisms, (4) wavelength selection, (5) polarization effects and control, (6) laser to integrated optics coupling,(7) fiber optic waveguides to integrated optics coupling, (8) souces, (9) detectors. The best materials, technology and processes for fabrication of integrated optical components for communications and fiber gyro applications are recommended.
Integrated vs. Federated Search
DEFF Research Database (Denmark)
Løvschall, Kasper
2009-01-01
Oplæg om forskelle og ligheder mellem integrated og federated search i bibliotekskontekst. Holdt ved temadag om "Integrated Search - samsøgning i alle kilder" på Danmarks Biblioteksskole den 22. januar 2009.......Oplæg om forskelle og ligheder mellem integrated og federated search i bibliotekskontekst. Holdt ved temadag om "Integrated Search - samsøgning i alle kilder" på Danmarks Biblioteksskole den 22. januar 2009....
Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne
1988-01-01
The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.
Integration phenomena Paralympic cyclists
Diepoldová, Tereza
2017-01-01
Title: Integration phenomena Paralympic cyclists. Objectives of work: Try to find integration phenomena in relation to sport training and its impact on selected cyclists with disabilities. Methods: Case report structured interview, data collection method - the method of interrogation. Results: Based on case studies developed a structured interview, we found differences in the integration, which we have divided into phases - before obtaining disability, acclimatization, sports integration. Fur...
Pandey, Chandan
2015-01-01
This book is intended for developers who are either already involved with enterprise integration or planning to venture into the domain. Basic knowledge of Java and Spring is expected. For newer users, this book can be used to understand an integration scenario, what the challenges are, and how Spring Integration can be used to solve it. Prior experience of Spring Integration is not expected as this book will walk you through all the code examples.
Modern functional quantum field theory summing Feynman graphs
Fried, Herbert M
2013-01-01
A monograph, which can also be used as a textbook for graduate students, this book contains new and novel applications of Schwinger's well-known functional solutions, made possible by the use of Fradkin's little-known functional representations, together with recent research work of the author and his colleagues.
Selfconsistent Solution of Galitskii-Feynman Equations at Finite Temperature
International Nuclear Information System (INIS)
Bozek, P.
1999-01-01
Full text: We solve the in-medium T-matrix equation at finite temperature including the off-shell propagation of nucleons. In this way a self-consistent spectral function for the nucleons is obtained. The results are compared to a calculation using the quasiparticle approximation in the T-matrix equation. Also the effective in-medium cross sections for the two cases are compared. (author)
On the invariance of residues of Feynman graphs
International Nuclear Information System (INIS)
Bierenbaum, Isabella; Kreckel, Richard; Kreimer, Dirk
2002-01-01
We use simple iterated one-loop graphs in massless Yukawa theory and QED to pose the following question: what are the symmetries of the residues of a graph under a permutation of places to insert subdivergences. The investigation confirms partial invariance of the residue under such permutations: the highest weight transcendental is invariant under such a permutation. For QED this result is gauge invariant, i.e., the permutation invariance holds for any gauge. Computations are done making use of the Hopf algebra structure of graphs and employing GiNaC to automate the calculations
To Have Been a Student of Richard Feynman
Indian Academy of Sciences (India)
During the time that I was his doctoral student, he was writing his famous papers on the theory of positrons (with the backward-in-time paths) and on QED, which appeared together in the same issue of the Physical Review. He asked me to read them, to correct his terrible spelling and grammar, and to serve as a guinea pig.
Dark-matter bound states from Feynman diagrams
Petraki, K.; Postma, M.; Wiechers, M.
2015-01-01
If dark matter couples directly to a light force mediator, then it may form bound states in the early universe and in the non-relativistic environment of haloes today. In this work, we establish a field-theoretic framework for the computation of bound-state formation cross-sections, de-excitation
Five Things I Learned from Richard Feynman About Science ...
Indian Academy of Sciences (India)
One involved giving a report on research that had been done on cats. He was unfamiliar with the names of the muscles mentioned, so he went down to the library to get “a map of the cat”. Then he gave his report, beginning with an explanation of the cat's anatomy. The biology students immediately stopped him, saying they ...
Optimizing Computer Technology Integration
Dillon-Marable, Elizabeth; Valentine, Thomas
2006-01-01
The purpose of this study was to better understand what optimal computer technology integration looks like in adult basic skills education (ABSE). One question guided the research: How is computer technology integration best conceptualized and measured? The study used the Delphi method to map the construct of computer technology integration and…
Foundations for Psychotherapy Integration
Directory of Open Access Journals (Sweden)
António Branco Vasco
2014-10-01
Full Text Available The movement for integration in psychotheray is clearly one of the main trends that can be observed in the field. The author stresses three main reasons for this state of affairs and as a way of justifying the importance of integration: historical and psychosocial, empirical and philosophical. A specific way of thinking in integrative terms is also outlined - "paradigmatic complementarity."
Discrete bipolar universal integrals
Czech Academy of Sciences Publication Activity Database
Greco, S.; Mesiar, Radko; Rindone, F.
2014-01-01
Roč. 252, č. 1 (2014), s. 55-65 ISSN 0165-0114 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : bipolar integral * universal integral * Choquet integral Subject RIV: BA - General Mathematics Impact factor: 1.986, year: 2014 http://library.utia.cas.cz/separaty/2014/E/mesiar-0432224.pdf
Ahner, Henry
2009-01-01
Integration (here visualized as a pounding process) is mathematically realized by simple transformations, successively smoothing the bounding curve into a straight line and the region-to-be-integrated into an area-equivalent rectangle. The relationship to Riemann sums, and to the trapezoid and midpoint methods of numerical integration, is…
DEFF Research Database (Denmark)
Bygstad, Bendik; Nielsen, Peter Axel; Munkvold, Bjørn Erik
2010-01-01
. Expanding the perspective of traditional project management research, we draw extensively on central insights from IS research. Building on socio-technical IS research and Software Engineering research we suggest four generic patterns of integration: Big Bang, Stakeholder Integration, Technical Integration...
Curriculum Integration: An Overview
Wall, Amanda; Leckie, Alisa
2017-01-01
Curriculum integration is a tenet of middle level education. "This We Believe," the position paper of the Association for Middle Level Education, advocates for curriculum that is exploratory, relevant, integrative, and meaningful for young adolescents. Teachers can integrate curriculum across content areas by anchoring units of study in…
Steffensen's integral inequality for conformable fractional integrals
Directory of Open Access Journals (Sweden)
Mehmet Zeki Sarikaya
2017-09-01
Full Text Available The aim of this paper is to establish some Steffensen’s type inequalities for conformable fractional integral. The results presented here would provide generalizations of those given in earlier works.
Krainak, Michael; Merritt, Scott
2016-01-01
Integrated photonics generally is the integration of multiple lithographically defined photonic and electronic components and devices (e.g. lasers, detectors, waveguides passive structures, modulators, electronic control and optical interconnects) on a single platform with nanometer-scale feature sizes. The development of photonic integrated circuits permits size, weight, power and cost reductions for spacecraft microprocessors, optical communication, processor buses, advanced data processing, and integrated optic science instrument optical systems, subsystems and components. This is particularly critical for small spacecraft platforms. We will give an overview of some NASA applications for integrated photonics.
International Nuclear Information System (INIS)
Thatcher, D.
1989-01-01
The NRC has recognized the need to integrate generic issues (GIs). The GI process includes a number of phases, all of which should recognize the potential for overlap and conflict among related issues. In addition to the issues themselves, other related NRC and industry programs and activities need to be factored into the GI process. Integration has taken place, or is taking place, for a number of GIs. Each case of integration involves a specific set of circumstances and, as a result, the way in which integration proceeds can vary. This paper discusses the integration of issues in the generic issue process and provides a number of examples
DEFF Research Database (Denmark)
Pitkänen, Kati; Oratuomi, Joose; Hellgren, Daniela
Increased attention to, and careful planning of the integration of migrants into Nordic societies is ever more important. Nature based integration is a new solution to respond to this need. This report presents the results of a Nordic survey and workshop and illustrates current practices of nature...... based integration by case study descriptions from Denmark, Sweden Norway and Finland. Across Nordic countries several practical projects and initiatives have been launched to promote the benefits of nature in integration and there is also growing academic interest in the topic. Nordic countries have...... the potential of becoming real forerunners in nature based integration even at the global scale....
Entrepreneurial Integration Skills
DEFF Research Database (Denmark)
Bauer, Florian; Schriber, Svante; King, David R.
2016-01-01
Acquisition integration is important to realize synergies and to achieve acquisition success. However, there is a lack of clarity on pertinent integration approaches suggesting that integration is more complex and dynamic than traditionally assumed. In this chapter, we shed light on ambiguous cause...... effect relationships by investigating the effect of integration related decisions on intermediate goals. Additionally, we argue that entrepreneurial integration skills, or proactivity under ambiguity, are needed to keep pace with the dynamism inherent in acquisition integration. Based on primary data...... on 116 acquisitions, we find that entrepreneurial integration skills can display both advantages and disadvantages. While it helps to realize expected and serendipitous synergies, it can also trigger employee uncertainty due to decreased transparency. In supplementary analysis, we show measures...
Searching for integrable systems
International Nuclear Information System (INIS)
Cary, J.R.
1984-01-01
Lack of integrability leads to undesirable consequences in a number of physical systems. The lack of integrability of the magnetic field leads to enhanced particle transport in stellarators and tokamaks with tearing-mode turbulence. Limitations of the luminosity of colliding beams may be due to the onset of stochasticity. Enhanced radial transport in mirror machines caused by the lack of integrability and/or the presence of resonances may be a significant problem in future devices. To improve such systems one needs a systematic method for finding integrable systems. Of course, it is easy to find integrable systems if no restrictions are imposed; textbooks are full of such examples. The problem is to find integrable systems given a set of constraints. An example of this type of problem is that of finding integrable vacuum magnetic fields with rotational transform. The solution to this problem is relevant to the magnetic-confinement program
Immigrant Integration: Acculturation and Social Integration
Directory of Open Access Journals (Sweden)
Astrid HAMBERGER
2009-11-01
Full Text Available This article tackles the concept of “immigrant integration” as it is analyzed by different authors in the international migration field. In this article, I will use the terms “refugee” and “immigrant” as equivalent to each other due to the interchangeable character of these concepts throughout the integration literature. First, the article brings into discussion the definitional and conceptual battle around the concept of immigrant “integration”, and second, it will describe and analyze cultural and social integration with their presupposing processes.
Bugdol, Marek
2015-01-01
Examining the challenges of integrated management, this book explores the importance and potential benefits of using an integrated approach as a cross-functional concept of management. It covers not only standardized management systems (e.g. International Organization for Standardization), but also models of self-assessment, as well as different types of integration. Furthermore, it demonstrates how processes and systems can be integrated, and how management efficiency can be increased. The major part of this book focuses on management concepts which use integration as a key tool of management processes (e.g. the systematic approach, supply chain management, virtual and network organizations, processes management and total quality management). Case studies, illustrations, and tables are also provided to exemplify and illuminate the content, as well as examples of successful and failed integrations. Providing a particularly useful resource to managers and specialists involved in the improvement of organization...
Integration of reusable systems
Rubin, Stuart
2014-01-01
Software reuse and integration has been described as the process of creating software systems from existing software rather than building software systems from scratch. Whereas reuse solely deals with the artifacts creation, integration focuses on how reusable artifacts interact with the already existing parts of the specified transformation. Currently, most reuse research focuses on creating and integrating adaptable components at development or at compile time. However, with the emergence of ubiquitous computing, reuse technologies that can support adaptation and reconfiguration of architectures and components at runtime are in demand. This edited book includes 15 high quality research papers written by experts in information reuse and integration to cover the most recent advances in the field. These papers are extended versions of the best papers which were presented at IEEE International Conference on Information Reuse and Integration and IEEE International Workshop on Formal Methods Integration, which wa...
What constitutes information integrity?
Directory of Open Access Journals (Sweden)
S. Flowerday
2007-12-01
Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'
What constitutes information integrity?
Directory of Open Access Journals (Sweden)
S. Flowerday
2008-01-01
Full Text Available This research focused on what constitutes information integrity as this is a problem facing companies today. Moreover, information integrity is a pillar of information security and is required in order to have a sound security management programme. However, it is acknowledged that 100% information integrity is not currently achievable due to various limitations and therefore the auditing concept of reasonable assurance is adopted. This is in line with the concept that 100% information security is not achievable and the notion that adequate security is the goal, using appropriate countermeasures. The main contribution of this article is to illustrate the importance of and provide a macro view of what constitutes information integrity. The findings are in harmony with Samuel Johnson's words (1751: 'Integrity without knowledge is weak and useless, and knowledge without integrity is dangerous and dreadful.'
DEFF Research Database (Denmark)
Jørgensen, Tine Herreborg; Remmen, Arne; Mellado, M. Dolores
2006-01-01
of integration. The focus of the article is primarily to discuss three ambition levels of integration: from increased compatibility of system elements over coordination of generic processes to an embeddedness of an integrated management system (IMS) in a culture of learning and continuous improvements......Different approaches to integration of management systems (ISO 9001, ISO 14001, OHSAS 18001 and SA 8000) with various levels of ambition have emerged. The tendency of increased compatibility between these standards has paved the road for discussions of, how to understand the different aspects....... At present, national IMS standards are being developed, and the IMS standards in Denmark and Spain are being analysed regarding the ambition level for integration. Should the ISO organisation decide to make a standard for IMS, then it would be necessary to consider the different levels of integration...
Classical Mechanics and Symplectic Integration
DEFF Research Database (Denmark)
Nordkvist, Nikolaj; Hjorth, Poul G.
2005-01-01
Content: Classical mechanics: Calculus of variations, Lagrange’s equations, Symmetries and Noether’s theorem, Hamilton’s equations, cannonical transformations, integrable systems, pertubation theory. Symplectic integration: Numerical integrators, symplectic integrators, main theorem on symplectic...
Mikkelsen, Caroline; Olsen, Kristine Falk; Weng, Millie Cammilla; Andersen, Stine Bjørnstrup
2012-01-01
We found interest in this project, when we through the media discovered that there is a lot of prejudicesregardingimmigrants in Denmark. We saw a problem in these prejudices and wanted to get an insight in howthese prejudicesaffect the integration in Denmark, which led us to following question of reach: What are the problems about the Danish integration in relation to stigma and what part do the conquests play in the debate, regarding assimilation or integration in the Danish society. Our ...
Integrated Sensitivity Analysis Workflow
Energy Technology Data Exchange (ETDEWEB)
Friedman-Hill, Ernest J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hoffman, Edward L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gibson, Marcus J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Clay, Robert L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2014-08-01
Sensitivity analysis is a crucial element of rigorous engineering analysis, but performing such an analysis on a complex model is difficult and time consuming. The mission of the DART Workbench team at Sandia National Laboratories is to lower the barriers to adoption of advanced analysis tools through software integration. The integrated environment guides the engineer in the use of these integrated tools and greatly reduces the cycle time for engineering analysis.
International Nuclear Information System (INIS)
Kauffman, L.H.
1990-01-01
This paper gives a heuristic derivation of the skein relation for the Homfly polynomial in an integral formalism. The derivation is formally correct but highly simplified. In the light of Witten's proposal for invariants of links via functional integrals, it is useful to have a formal pattern to compare with the complexities of the full approach. The formalism is a heuristic. However, it is closely related to the actual structure of the Witten functional integral
International Nuclear Information System (INIS)
Gautier, G.M.
2002-01-01
This document presents the integrated reactors concepts by a presentation of four reactors: PIUS, SIR, IRIS and CAREM. The core conception, the operating, the safety, the economical aspects and the possible users are detailed. From the performance of the classical integrated PWR, the necessity of new innovative fuels utilization, the research of a simplified design to make easier the safety and the KWh cost decrease, a new integrated reactor is presented: SCAR 600. (A.L.B.)
Modularly Integrated MEMS Technology
National Research Council Canada - National Science Library
Eyoum, Marie-Angie N
2006-01-01
Process design, development and integration to fabricate reliable MEMS devices on top of VLSI-CMOS electronics without damaging the underlying circuitry have been investigated throughout this dissertation...
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Avionics systems integration technology
Stech, George; Williams, James R.
1988-01-01
A very dramatic and continuing explosion in digital electronics technology has been taking place in the last decade. The prudent and timely application of this technology will provide Army aviation the capability to prevail against a numerically superior enemy threat. The Army and NASA have exploited this technology explosion in the development and application of avionics systems integration technology for new and future aviation systems. A few selected Army avionics integration technology base efforts are discussed. Also discussed is the Avionics Integration Research Laboratory (AIRLAB) that NASA has established at Langley for research into the integration and validation of avionics systems, and evaluation of advanced technology in a total systems context.
Extending Database Integration Technology
National Research Council Canada - National Science Library
Buneman, Peter
1999-01-01
Formal approaches to the semantics of databases and database languages can have immediate and practical consequences in extending database integration technologies to include a vastly greater range...
Integrated Information Management (IIM)
National Research Council Canada - National Science Library
McIlvain, Jason
2007-01-01
Information Technology is the core capability required to align our resources and increase our effectiveness on the battlefield by integrating and coordinating our preventative measures and responses...
Building integrated photovoltaic; Photovaltaique integre aux batiments
Energy Technology Data Exchange (ETDEWEB)
NONE
2004-01-01
Durable, modular and flexible in use, as demonstrated by the different case studies in this publication, photovoltaic can replace diverse building elements, from glass facades to weather proof roofs. This leaflet towards architects describes aesthetic, technical, economic and environmental interest of building integrated photovoltaic. (author)
Wealth Through Integration: Regional Integration and Poverty ...
International Development Research Centre (IDRC) Digital Library (Canada)
2013-02-27
Feb 27, 2013 ... Could regional integration be a first step toward joining the global market? Since trade liberalization reduces revenues from duties and taxes, the available resources for public investments are negatively affected. The proposed solution encourages less-developed countries to emphasize regional ...
Factorization of Behavioral Integrity
DEFF Research Database (Denmark)
Li, Ximeng; Nielson, Flemming; Nielson, Hanne Riis
2015-01-01
We develop a bisimulation-based nonintereference property that describes the allowed dependencies between communication behaviors of different integrity levels. The property is able to capture all possible combinations of integrity levels for the “presence” and “content” of actual communications...
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko
2005-01-01
Roč. 28, č. 156 (2005), s. 365-370 ISSN 0165-0114 R&D Projects: GA ČR(CZ) GA402/04/1026 Institutional research plan: CEZ:AV0Z10750506 Keywords : fuzzy measures * fuzzy integral * regular fuzzy integral Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005
Hermeneutics of Integrative Knowledge.
Shin, Un-chol
This paper examines and compares the formation processes and structures of three types of integrative knowledge that in general represent natural sciences, social sciences, and humanities. These three types can be observed, respectively, in the philosophies of Michael Polanyi, Jurgen Habermas, and Paul Ricoeur. These types of integrative knowledge…
2010-09-01
Thermal Management (Propulsion a vitesse elevee : Conception du moteur - integration et gestion thermique ) 14. ABSTRACT These notes deal with the...analogy for heat transfer from the outer flow to the conical intake shell via the Ramjets: Airframe Integration 6 - 24 RTO-EN-AVT-185 boundary
Integrated Marketing Communications
Black, Jim
2004-01-01
Integration has become a cliche in enrollment management and student services circles. The term is used to describe everything from integrated marketing to seamless services. Often, it defines organizational structures, processes, student information systems, and even communities. In Robert Sevier's article in this issue of "College and…
Integration and Polar Coordinates
Indian Academy of Sciences (India)
Jacobian matrix, Riemann- integrable function, co-area for- mula, Lipschitzfunction, levelset. S Kesavan. A simple proof of the formula for the integration of radial functions on R", N > 2, is given. As an application, the volume of the N-dimensional unit ball is computed. 1. Introduction. The method of substitution, also known as ...
Jaco Dagevos; Mérove Gijsberts
2007-01-01
Original title: Jaarrapport integratie 2007. The Annual Report on Integration 2007 describes the integration of non-Western ethnic minorities in the Netherlands using a wide range of indicators. It focuses among other things on the situation of ethnic minority pupils in education, the
Directory of Open Access Journals (Sweden)
D. Naylor
1986-01-01
Full Text Available This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.
International Nuclear Information System (INIS)
Chang, Y.I.; Marchaterre, J.F.; Sevy, R.H.
1984-01-01
Key features of the IFR consist of a pool-type plant arrangement, a metal fuel-based core design, and an integral fuel cycle with colocated fuel cycle facility. Both the basic concept and the technology base have been demonstrated through actual integral cycle operation in EBR-II. This paper discusses the inherent safety characteristics of the IFR concept
The Fresnel Integrals Revisited
Chen, Hongwei
2009-01-01
This note presents another elementary method to evaluate the Fresnel integrals. It is interesting to see that this technique is also strong enough to capture a number of pairs of parameter integrals. The main ingredients of the method are the consideration of some related derivatives and linear differential equations.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
The properties of path integrals associated with the allowance for nonstandard terms reflecting the operator nature of the canonical variables are considered. Rules for treating such terms (''equivalence rules'') are formulated. Problems with a boundary, the behavior of path integrals under canonical transformations, and the problem of quantization of dynamical systems with constraints are considered in the framework of the method
DEFF Research Database (Denmark)
Rendtorff, Jacob Dahl
2015-01-01
Integrity can be defined in the following sense: Integrity accounts for the inviolability of the human being. Although originally a virtue of uncorrupted character, expressing uprightness, honesty, and good intentions, it has, like dignity, been universalized as a quality of the person as such. T...
Integral transformational coaching
Keizer, W.A.J.; Nandram, S.S.
2009-01-01
In Chap. 12, Keizer and Nandram present the concept of Integral Transformational Coaching based on the concept of Flow and its effects on work performance. Integral Transformational Coaching is a method that prevents and cures unhealthy stress and burnout. They draw on some tried and tested
DEFF Research Database (Denmark)
Markvorsen, Steen
2010-01-01
-integralerne. Undervejs introduceres \\texttt{Integrator8}. Det er en pakke med Maple procedurer, som er udviklet specielt med henblik på eksempelbaseret visuel læring af de indledende integrationsbegreber og deres mangfoldige anvendelser. Vi giver eksempler på, hvordan integration i flere variable anvendes til beregning...
DEFF Research Database (Denmark)
Holst, Finn
2010-01-01
Evaluering af projektet Musik, Sprog og Integration, Søndermarkskolen, Horsens. Andenårsevaluering af et treårigt projekt.......Evaluering af projektet Musik, Sprog og Integration, Søndermarkskolen, Horsens. Andenårsevaluering af et treårigt projekt....
Kanonisk sikkerhed og integration
DEFF Research Database (Denmark)
Larsen, Vibe; Øland, Trine
2006-01-01
Artiklen diskuterer, med indragelse af den lignende debat i andre europæiske lande, kulturkanonen i forhold til integration......Artiklen diskuterer, med indragelse af den lignende debat i andre europæiske lande, kulturkanonen i forhold til integration...
Energy Technology Data Exchange (ETDEWEB)
Hira, A.; Amaya, L. [Simon Fraser University, Burnaby, BC (Canada). Dept. of Political Science
2003-01-01
Amidst the international movement to privatize and deregulate electricity and gas sectors of economics, the question of the integration of those sectors has been somewhat underestimated. In fact, the integration of energy markets across boundaries is occurring. We examine this process in three regions: Europe, Central America, and South America. We analyze the forces driving integration in each area, and estimate the prospects for progress. We take a close look at Nordpool, which is now the most integrated market in the world, to see if it can serve as a model for other regions. We close with a set of conditions that we suggest are necessary for a successful international integration of energy markets. (author)
International Nuclear Information System (INIS)
Hira, Anil; Amaya, Libardo
2003-01-01
Amidst the international movement to privatize and deregulate electricity and gas sectors of economies, the question of the integration of those sectors has been somewhat underestimated. In fact, the integration of energy markets across boundaries is occurring. We examine this process in three regions: Europe, Central America, and South America. We analyze the forces driving integration in each area, and estimate the prospects for progress. We take a close look at Nordpool, which is now the most integrated market in the world, to see if it can serve as a model for other regions. We close with a set of conditions that we suggest are necessary for a successful international integration of energy markets
DEFF Research Database (Denmark)
Fogelman, Tatiana
Over the past fifteen years the district of Berlin-Marzahn became home to the largest concentration of post-Soviet migrants of German ancestry in the former East Germany. Drawing on my research in the district, including two of its integration projects for middle-aged, unemployed migrants, I...... examine these projects’ failed attempts to create spaces of encounter between the migrants and district’s long-term residents. In this presentation I focus specifically on the structural position of integration work (Integrationsarbeit) that creates first and foremost conditions of possibility for its...... temporal imaginaries underpinning the ideas of integration through encounter, as well as integration more broadly, I argue for reflexivity-centric public reformulations of both integration and encounter....
Personal Integrity and Leadership
Directory of Open Access Journals (Sweden)
Antonius Gea
2016-07-01
Full Text Available Generally, integrity is associated with leadership, especially in the organization or company. Integrity in leadership becomes a growing concern in business and organizations. The aim of this study was to find out the connection that could be shaped between personal integrity and the skill of leadership especially in the performance of work. This study used a library research, a literature study that done by using the available resources and relevant literature, related to the topic being discussed by the author. Books or journal articles related to topics were used as background reading to understand well about the problems of integrity and leadership, especially in the organization or company. This study finds out that the leader integrity is related to follower work role performance and that this effect is fully mediated through follower affective organizational commitment.
Neuroeconomics and Integrated Care
DEFF Research Database (Denmark)
Larsen, Torben
2012-01-01
Background: Fragmented specialized care for the frail elderly as claimed by WHO needs horizontal integration across settings. The home of the patient seems to be a promising place to integrate hospital care, primary care and social services for high-risk discharges where the quality...... of rehabilitation makes a difference. Objective: The study aims to reveal how integrated home care may be organised to improve quality of care as compared to usual hospital care. Method: A qualitative case study of the use of a neuroeconomic model in relation to multidisciplianry collaboration on a RCT...... of integrated home care for stroke patients. Results: (1) The classical understanding of CNS is that of a dual system of ANS and Cortex. The new neuroeconomic understanding is that of a reciprocal balance of Limbic System (LS) and Neocortex (NC). This applies directly in favour of integrated homecare compared...
Retroviral integration: Site matters
Demeulemeester, Jonas; De Rijck, Jan
2015-01-01
Here, we review genomic target site selection during retroviral integration as a multistep process in which specific biases are introduced at each level. The first asymmetries are introduced when the virus takes a specific route into the nucleus. Next, by co‐opting distinct host cofactors, the integration machinery is guided to particular chromatin contexts. As the viral integrase captures a local target nucleosome, specific contacts introduce fine‐grained biases in the integration site distribution. In vivo, the established population of proviruses is subject to both positive and negative selection, thereby continuously reshaping the integration site distribution. By affecting stochastic proviral expression as well as the mutagenic potential of the virus, integration site choice may be an inherent part of the evolutionary strategies used by different retroviruses to maximise reproductive success. PMID:26293289
Vertcal integration: origins of oil industry integration
International Nuclear Information System (INIS)
Rainbow, R.
2001-01-01
This article examines the structure of the US oil industry in relation to the history of the industry, capital market assumptions, and advice on the enhancement of 'shareholder value'. The driving forces behind the attempts to establish cartels and vertical integration are considered, and the emergence of US companies resulting from the break-up of the Standard Oil Trust cartel, the influence of costs and logistics on the structure of the industry outside the USA , and the structure of the natural gas industry are discussed along with the discovery of large Middle East oil reserves, the enormous growth in demand for oil products in Europe and Japan, and the formation of the OPEC cartel. Details are given of the breaking down of vertical integration in the big oil companies, the theory of conglomerates, the success of big companies, the importance of scale to balance exploration risks, and the need to adjust in time to shifts in the business environment
Long Pulse Integrator of Variable Integral Time Constant
International Nuclear Information System (INIS)
Wang Yong; Ji Zhenshan; Du Xiaoying; Wu Yichun; Li Shi; Luo Jiarong
2010-01-01
A kind of new long pulse integrator was designed based on the method of variable integral time constant and deducting integral drift by drift slope. The integral time constant can be changed by choosing different integral resistors, in order to improve the signal-to-noise ratio, and avoid output saturation; the slope of integral drift of a certain period of time can be calculated by digital signal processing, which can be used to deduct the drift of original integral signal in real time to reduce the integral drift. The tests show that this kind of long pulse integrator is good at reducing integral drift, which also can eliminate the effects of changing integral time constant. According to experiments, the integral time constant can be changed by remote control and manual adjustment of integral drift is avoided, which can improve the experiment efficiency greatly and can be used for electromagnetic measurement in Tokamak experiment. (authors)
Application of FIRE for the calculation of photon matrix elements
Indian Academy of Sciences (India)
In order to evaluate the two-loop Feynman diagrams for the photon matrix element of the gluon operator, I apply the recently developed algorithm FIRE which reduces a complicated sum of scalar Feynman integrals to a linear combination of a few master integrals. The details of the calculation are presented.
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-04-01
Integrated assessment can be used to evaluate and clarify resource management policy options and outcomes for decision makers. The defining characteristics of integrated assessment are (1) focus on providing information and analysis that can be understood and used by decision makers rather than for merely advancing understanding and (2) its multidisciplinary approach, using methods, styles of study, and considerations from a broader variety of technical areas than would typically characterize studies produced from a single disciplinary standpoint. Integrated assessment may combine scientific, social, economic, health, and environmental data and models. Integrated assessment requires bridging the gap between science and policy considerations. Because not everything can be valued using a single metric, such as a dollar value, the integrated assessment process also involves evaluating trade-offs among dissimilar attributes. Scientists at Oak Ridge National Laboratory (ORNL) recognized the importance and value of multidisciplinary approaches to solving environmental problems early on and have pioneered the development of tools and methods for integrated assessment over the past three decades. Major examples of ORNL`s experience in the development of its capabilities for integrated assessment are given.
Three dimensional system integration
Papanikolaou, Antonis; Radojcic, Riko
2010-01-01
Three-dimensional (3D) integrated circuit (IC) stacking is the next big step in electronic system integration. It enables packing more functionality, as well as integration of heterogeneous materials, devices, and signals, in the same space (volume). This results in consumer electronics (e.g., mobile, handheld devices) which can run more powerful applications, such as full-length movies and 3D games, with longer battery life. This technology is so promising that it is expected to be a mainstream technology a few years from now, less than 10-15 years from its original conception. To achieve thi
DEFF Research Database (Denmark)
Val, Maria Rosa Rovira; Lehmann, Martin; Zinenko, Anna
dramatically with many of the world’s economies facing downturn and a looming possible recession; and the global economic and political balance changing; (ii) most larger companies and quite a few SMEs now have a mature knowledge of these standards; and (iii) some standards are advocating for integration...... procedures, such as cases of for example ISO integrated management systems, mutual equivalences recognition of Global Compact-GRI-ISO26000, or the case of IIRC initiative to develop integrated reporting on an organization’s Financial, Environmental, Social and Governance performance. This paper focuses...
SQL Server Integration Services
Hamilton, Bill
2007-01-01
SQL Server 2005 Integration Services (SSIS) lets you build high-performance data integration solutions. SSIS solutions wrap sophisticated workflows around tasks that extract, transform, and load (ETL) data from and to a wide variety of data sources. This Short Cut begins with an overview of key SSIS concepts, capabilities, standard workflow and ETL elements, the development environment, execution, deployment, and migration from Data Transformation Services (DTS). Next, you'll see how to apply the concepts you've learned through hands-on examples of common integration scenarios. Once you've
Social integration i arbejdslivet
DEFF Research Database (Denmark)
Nielsen, Kjeld; Christensen, Allan
2002-01-01
of the study that social integration depends on working environment conditions as well as cultural conditions. The social integration again is crucial for the way in which employees perceive the daily work situation and indirectly also for the well-being of the clients of the institution.......The study reported in this article is based on a combination of methods related to working environment and to organisational culture. The combination is aimed at studying the extent and meaning of the social integration of the employees in an institution for handicapped adults. It is the conclusion...
Roussos, Ioannis Markos
2013-01-01
Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineering problems.The book contains the necessary background, theorems, and tools, along with two lists of the most important integrals and sums computed in the text. Numerous examples at various levels of difficulty illustrate the concepts and theorems. The
The Structural Integrity Centre
International Nuclear Information System (INIS)
Tomkins, B.
1987-01-01
The paper concerns the development and work of the Structural Integrity Centre (SIC) at Risley Nuclear Laboratories, United Kingdom. The centre was set up to provide authoritative advice to plant designers and operators on the integrity and life assessment of structures and components across the reactor projects in the United Kingdom. A description is given of the structure and role of the SIC, as well as the Structural Integrity Assessment work. The assessment methods are described for thermally loaded structures and welded structures. Finally, defect significance assessment and environmental effects are outlined. (U.K.)
Principles of data integration
Doan, AnHai; Ives, Zachary
2012-01-01
How do you approach answering queries when your data is stored in multiple databases that were designed independently by different people? This is first comprehensive book on data integration and is written by three of the most respected experts in the field. This book provides an extensive introduction to the theory and concepts underlying today's data integration techniques, with detailed, instruction for their application using concrete examples throughout to explain the concepts. Data integration is the problem of answering queries that span multiple data sources (e.g., databases, web
Wolfendale, E
2013-01-01
MOS Integral Circuit Design aims to help in the design of integrated circuits, especially large-scale ones, using MOS Technology through teaching of techniques, practical applications, and examples. The book covers topics such as design equation and process parameters; MOS static and dynamic circuits; logic design techniques, system partitioning, and layout techniques. Also featured are computer aids such as logic simulation and mask layout, as well as examples on simple MOS design. The text is recommended for electrical engineers who would like to know how to use MOS for integral circuit desi
International Nuclear Information System (INIS)
DeWitt-Morette, C.
1983-01-01
Much is expected of path integration as a quantization procedure. Much more is possible if one recognizes that path integration is at the crossroad of stochastic and differential calculus and uses the full power of both stochastic and differential calculus in setting up and computing path integrals. In contrast to differential calculus, stochastic calculus has only comparatively recently become an instrument of thought. It has nevertheless already been used in a variety of challenging problems, for instance in the quantization problem. The author presents some applications of the stochastic scheme. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Kelley, C.T.; Xue, Z.Q. [North Carolina State Univ., Raleigh, NC (United States)
1994-12-31
Many discretizations of integral equations and compact fixed point problems are collectively compact and strongly convergent in spaces of continuous functions. These properties not only lead to stable and convergent approximations but also can be used in the construction of fast multilevel algorithms. Recently the GMRES algorithm has become a standard coarse mesh solver. The purpose of this paper is to show how the special properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to strengthen the norm in which convergence takes place. The authors illustrate these ideas with composite Gauss rules for integral equations on the unit interval.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Introduction to integral discriminants
International Nuclear Information System (INIS)
Morozov, A.; Shakirov, Sh.
2009-01-01
The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J n|r (S) = ∫e -S(x 1 ,...,x n ) dx 1 ...dx n . Actually, S-dependence remains the same if e -S in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate J n|r in a number of non-Gaussian cases. Using Ward identities - linear differential equations, satisfied by integral discriminants - we calculate J 2|3 ,J 2|4 ,J 2|5 and J 3|3 . In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.
Financial Integrity Benchmarks
City of Jackson, Mississippi — This data compiles standard financial integrity benchmarks that allow the City to measure its financial standing. It measure the City's debt ratio and bond ratings....
Rauscher, Anton
2003-01-01
Immigration und Integration : eine Herausforderung für Kirche, Gesellschaft und Politik in Deutschland und den USA / hrsg. von Anton Rauscher. - Berlin : Duncker & Humblot, 2003. - 174 S. - (Soziale Orientierung ; 15)
Integrated Health Management Definitions
National Aeronautics and Space Administration — The Joint Army Navy NASA Air Force Modeling and Simulation Subcommittee's Integrated Health Management panel was started about 6 years ago to help foster...
Federal Laboratory Consortium — Located near the center of the 586-square-mile Hanford Site is the Integrated Disposal Facility, also known as the IDF.This facility is a landfill similar in concept...
DEFF Research Database (Denmark)
Strandberg-Larsen, Martin
2011-01-01
differences were found in the perception of clinical integration in the two settings. More primary care clinicians in the Northern California region of Kaiser Permanente reported being part of a clinical integrated environment than did Danish general practitioners. By measuring the level of clinical...... respond to these needs, patients and providers face the multiple challenges of today's healthcare environment. Decision makers, planners and managers need evidence based policy options and information on the scope of the integrated care challenges they are facing. The US managed care organization Kaiser...... Permanente has been put forward as an example for European healthcare systems to follow, although the evidence base is far from conclusive. The thesis has five objectives: 1) To contribute to the understanding of the concept of integration in healthcare systems and to identify measurement methods to capture...
Funkhouser, John; Deslich, Barbara J.
2000-01-01
Explains the implementation of forensic science in an integrated curriculum and discusses the advantages of this approach. Lists the forensic science course syllabi studied in three high schools. Discusses the unit on polymers in detail. (YDS)
State Program Integrity Reviews
U.S. Department of Health & Human Services — State program integrity reviews play a critical role in how CMS provides effective support and assistance to states in their efforts to combat provider fraud and...
Chester, A; Bertolotti, M
1994-01-01
This volwne contains the Proceedings of a two-week summer conference titled "Advances in Integrated Optics" held June 1-9, 1993, in Erice, Sicily. This was the 18th annual course organized by the International School of Quantum Electronics, under the auspices of the "Ettore Majorana" Centre for Scientific Culture. The term Integrated Optics signifies guided-wave optical circuits consisting of two or more devices on a single substrate. Since its inception in the late 1960's, Integrated Optics has evolved from a specialized research topic into a broad field of work, ranging from basic research through commercial applications. Today many devices are available on market while a big effort is devolved to research on integrated nonlinear optical devices. This conference was organized to provide a comprehensive survey of the frontiers of this technology, including fundamental concepts, nonlinear optical materials, devices both in the linear and nonlinear regimes, and selected applications. These Proceedings update a...
Integrated Surface Dataset (Global)
National Oceanic and Atmospheric Administration, Department of Commerce — The Integrated Surface (ISD) Dataset (ISD) is composed of worldwide surface weather observations from over 35,000 stations, though the best spatial coverage is...
Integration, measure and probability
Pitt, H R
2012-01-01
Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
Huston, James A.
1971-01-01
Recounts the history and problems of European Economic Integration from the first post World War II organization, the OEEC, to the EEC (Common Market) and the EFTA. Suggestions for further reading are included. (JB)
Babusci, D.; Dattoli, G.; Germano, B.; Martinelli, M. R.; Ricci, P. E.
2011-01-01
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
Integrated inventory information system
Digital Repository Service at National Institute of Oceanography (India)
Sarupria, J.S.; Kunte, P.D.
The nature of oceanographic data and the management of inventory level information are described in Integrated Inventory Information System (IIIS). It is shown how a ROSCOPO (report on observations/samples collected during oceanographic programme...
DEFF Research Database (Denmark)
Strandberg-Larsen, Martin
2011-01-01
respond to these needs, patients and providers face the multiple challenges of today's healthcare environment. Decision makers, planners and managers need evidence based policy options and information on the scope of the integrated care challenges they are facing. The US managed care organization Kaiser...... Permanente has been put forward as an example for European healthcare systems to follow, although the evidence base is far from conclusive. The thesis has five objectives: 1) To contribute to the understanding of the concept of integration in healthcare systems and to identify measurement methods to capture...... the multi-dimensional aspects of integrated healthcare delivery. 2) To assess the level of integration of the Danish healthcare system. 3) To assess the use of joint health plans as a tool for coordination between the regional and local level in the Danish healthcare system. 4) To compare the inputs...
Integration a functional approach
Bichteler, Klaus
1998-01-01
This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might...
Systems Integration Fact Sheet
Energy Technology Data Exchange (ETDEWEB)
None
2016-06-01
This fact sheet is an overview of the Systems Integration subprogram at the U.S. Department of Energy SunShot Initiative. The Systems Integration subprogram enables the widespread deployment of safe, reliable, and cost-effective solar energy technologies by addressing the associated technical and non-technical challenges. These include timely and cost-effective interconnection procedures, optimal system planning, accurate prediction of solar resources, monitoring and control of solar power, maintaining grid reliability and stability, and many more. To address the challenges associated with interconnecting and integrating hundreds of gigawatts of solar power onto the electricity grid, the Systems Integration program funds research, development, and demonstration projects in four broad, interrelated focus areas: grid performance and reliability, dispatchability, power electronics, and communications.
Cohn, Hans M.
1983-01-01
Argues that although the executive has many tasks, he or she must view internal organizational integration as a primary task, making use of organizational charts, job descriptions, statements of goals and objectives, evaluations, and feedback devices. (RH)
International Nuclear Information System (INIS)
Itzykson, C.
1992-01-01
Some mathematical results are described on a remarkable application of matrix interaction due to Witten and Kontsevich, to study topological invariants. Some interesting properties of the Kontsevich integrals are identified. (K.A.) 4 refs
Pair Correlation Function Integrals
DEFF Research Database (Denmark)
Wedberg, Nils Hejle Rasmus Ingemar; O'Connell, John P.; Peters, Günther H.J.
2011-01-01
We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long-d...... distribution function has structure beyond the sampling limit imposed by the system size, the integration is more reliable, and usually more accurate, than simple integral truncation.......We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long......, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report...
Introduction to integral discriminants
Morozov, A.; Shakirov, Sh.
2009-12-01
The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant Jn|r(S) = ∫e-S(x1,...,xn)dx1...dxn. Actually, S-dependence remains the same if e-S in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate Jn|r in a number of non-Gaussian cases. Using Ward identities — linear differential equations, satisfied by integral discriminants — we calculate J2|3,J2|4,J2|5 and J3|3. In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.
2016-01-01
The integration of a DNA copy of the viral RNA genome into host chromatin is the defining step of retroviral replication. This enzymatic process is catalyzed by the virus-encoded integrase protein, which is conserved among retroviruses and LTR-retrotransposons. Retroviral integration proceeds via two integrase activities: 3′-processing of the viral DNA ends, followed by the strand transfer of the processed ends into host cell chromosomal DNA. Herein we review the molecular mechanism of retroviral DNA integration, with an emphasis on reaction chemistries and architectures of the nucleoprotein complexes involved. We additionally discuss the latest advances on anti-integrase drug development for the treatment of AIDS and the utility of integrating retroviral vectors in gene therapy applications. PMID:27198982
Complementary and Integrative Medicine
... medical treatments that are not part of mainstream medicine. When you are using these types of care, it may be called complementary, integrative, or alternative medicine. Complementary medicine is used together with mainstream medical ...
Integrated Reporting Information System -
Department of Transportation — The Integrated Reporting Information System (IRIS) is a flexible and scalable web-based system that supports post operational analysis and evaluation of the National...
Integrating corpora and dictionaries
DEFF Research Database (Denmark)
Kristoffersen, Jette Hedegaard; Troelsgård, Thomas
2012-01-01
In this paper, we will discuss different possibilities for integration of corpus data with dictionary data, mainly seen from a lexicographic point of view and in a sign language context. For about 25 years a text corpus has been considered a useful, if not necessary tool for editing dictionaries...... of written and spoken languages. Corpora are equally useful to sign language lexicographers, but sign language corpora have not become accessible until recent years. Nowadays corpora exist, or are being developed, for several sign languages, and we have the possibility of editing new, truly corpus-based sign...... language dictionaries, and of developing interfaces that integrate corpus and dictionary data. After a brief look at three existing integrated interfaces, one for German, one for Danish, and one for Danish Sign Language, we point out some of the problems that should be considered when making an integrated...
Francisco Javier Rodríguez Román
2012-01-01
Penitentiary integral defense is a set of techniques designed to solve the breach of the peace that may appear in the penitentiary world. This paper studies the scope and legal framework of penitentiary self-defense. This kind of self-defense is defined by the particular characteristics of a confinement context and a very specific regulation aimed at preserving the integrity of prisoners and penitentiary staff as well as prison facilities. A technical section illustrating the main penitentiar...
Integrated parasite management
DEFF Research Database (Denmark)
Clausen, Jesper Hedegaard; Madsen, Henry; Van, Phan Thi
2015-01-01
communities at risk through mass drug administration. However, we argue that treatment alone will not reduce the risk from eating infected fish and that sustainable effective control must adopt an integrated FZT control approach based on education, infrastructure improvements, and management practices...... that target critical control points in the aquaculture production cycle identified from a thorough understanding of FZT and host biology and epidemiology. We present recommendations for an integrated parasite management (IPM) program for aquaculture farms....
Energy Technology Data Exchange (ETDEWEB)
Clifford, David J.; Harris, James M.
2014-12-01
This is the IDC Re-Engineering Phase 2 project Integrated Master Plan (IMP). The IMP presents the major accomplishments planned over time to re-engineer the IDC system. The IMP and the associate Integrated Master Schedule (IMS) are used for planning, scheduling, executing, and tracking the project technical work efforts. REVISIONS Version Date Author/Team Revision Description Authorized by V1.0 12/2014 IDC Re- engineering Project Team Initial delivery M. Harris
Function integrated track system
Hohnecker, Eberhard
2010-01-01
The paper discusses a function integrated track system that focuses on the reduction of acoustic emissions from railway lines. It is shown that the combination of an embedded rail system (ERS), a sound absorbing track surface, and an integrated mini sound barrier has significant acoustic advantages compared to a standard ballast superstructure. The acoustic advantages of an embedded rail system are particularly pronounced in the case of railway bridges. Finally, it is shown that a...
DEFF Research Database (Denmark)
Rytter, Mikkel
2018-01-01
The article addresses some of the problems related to the concept of integration, which has been used (and abused) in Denmark since the 1980s to discuss socio-economic, cultural and religious challenges related to the everyday life of ethnic minorities. The concept of integration is not innocent,......-Lughod’s seminal article “writing against culture”, the article suggests strategies of “writing against integration” in order to regain the critical potential of academic analysis....
International Nuclear Information System (INIS)
Felder, Giovanni; Riser, Roman
2004-01-01
We study a class of holomorphic matrix models. The integrals are taken over middle-dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a measure with support on a collection of arcs in the complex planes. We show that the arcs are level sets of the imaginary part of a hyperelliptic integral connecting branch points
Integrated Electric Gas Turbine
Millsaps, Knox T.
2010-01-01
Patent An integrated electric gas turbine comprises a compressor that includes a plurality of airfoils. An electric motor is arranged to drive the compressor, and a combustor is arranged to receive compressed air from the compressor and further arranged to receive a fuel input. A turbine is arranged to receive the combustion gases from the combustor. A generator is integrated with the turbine and arranged to provide a power output. A controller is connected between the...
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko; Li, J.; Pap, E.
2013-01-01
Roč. 54, č. 3 (2013), s. 357-364 ISSN 0888-613X R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : concave integral * pseudo-addition * pseudo- multiplication Subject RIV: BA - General Mathematics Impact factor: 1.977, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-discrete pseudo-integrals. pdf
Experimental integrated photovoltaic systems
International Nuclear Information System (INIS)
Pop-Jordanov, Jordan; Markovska, Natasha; Dimitrov, D.; Kocev, K.; Dimitrovski, D.
2000-01-01
Recently, the interest in building-integrated photovoltaic installations has started to increase within governmental and municipality authorities, as well as some industrial companies. To serve a national public-awareness program of solar electricity promotion and education, the indigenous solar energy potential, optimization of possible PV installation, and three test cases of building-integrated grid-connected experimental facilities have been studied. The results showed the feasibility and performance of the proposed concepts. (Original)
Agroecology : integration with livestock
Tichit, Muriel; Lecompte, Philippe; Dumont, Bertrand
2014-01-01
Livestock systems are a large global asset contributing to food security and poverty alleviation, but livestock supply chains have major environmental impacts at global scale. The scientific literature on agroecology has not yet integrated livestock systems; only 5 percent of the indexed studies concerning agroecology deal with livestock. Following Dumont et al. (2013), we review five principles for integrating livestock systems within the agroecology debate: (i) adopting management practices...
HETEROGENEOUS INTEGRATION TECHNOLOGY
2017-08-24
9.1.1 FET- BT -HBT Integration........................................................................................... 22 9.1.2 Early GaAs-Si...Fabricated with Different Device Types on Separate Chips are Combined on the Same Chip in 2D SoC [26] 9.1.1 FET- BT -HBT Integration The semiconductor...electronics started with the use of bipolar transistors ( BTs ) but field effect transistors (FETs) were later introduced for digital applications. As
Heterogeneous Integration Technology
2017-05-19
This type of packaging is used in mobile products where because of space saving features and can be found in smart phones and tables. Figure 69...picture of 8-strata stacked chips with TSVs on interposer layer [128]. ............................. 59 Figure 72: The DARPA SMART program: (a...mounted die is integrated with another package containing stacked chips with bond wire connections [153]. PoP integration is also used heavily in smart
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
Integrated smart structures wingbox
Simon, Solomon H.
1993-09-01
One objective of smart structures development is to demonstrate the ability of a mechanical component to monitor its own structural integrity and health. Achievement of this objective requires the integration of different technologies, i.e.: (1) structures, (2) sensors, and (3) artificial intelligence. We coordinated a team of experts from these three fields. These experts used reliable knowledge towards the forefront of their technologies and combined the appropriate features into an integrated hardware/software smart structures wingbox (SSW) test article. A 1/4 in. hole was drilled into the SSW test article. Although the smart structure had never seen damage of this type, it correctly recognized and located the damage. Based on a knowledge-based simulation, quantification and assessment were also carried out. We have demonstrated that the SSW integrated hardware & software test article can perform six related functions: (1) identification of a defect; (2) location of the defect; (3) quantification of the amount of damage; (4) assessment of performance degradation; (5) continued monitoring in spite of damage; and (6) continuous recording of integrity data. We present the successful results of the integrated test article in this paper, along with plans for future development and deployment of the technology.
APPROACHES TO PUBLIC INTEGRITY
Directory of Open Access Journals (Sweden)
Simona-Roxana ULMAN
2015-08-01
Full Text Available Both concepts, integrity and public integrity, are always asked qualities in the social and economic environment, but they are never well defined. In this context, finding precise definitions and offering an ample explanation of the concepts are desired and useful for both economic theoretical and practical levels and become the aim of the present paper. Without a good understanding of a concept, no one is capable to attain it. In this context, it is impossible to ask for a public sector of integrity if both public actors and the citizens do not know what it really means. Therefore, the public actors first have to understand what integrity really supposes, and, then, to be capable to respect its principles. Taking into consideration the effects of public integrity or, on its opposite, of the divergence from it, especially represented by the phenomenon of corruption, on the economy at the macro, but also, on the micro level, public integrity in itself becomes a real economic problem that is aimed to be extensively analyzed through our interdisciplinary approach.
Fostering Integrity in Research
McNutt, M. K.
2017-12-01
The responsible conduct of research requires that all involved in the research enterprise - researchers, sponsors, reviewers, publishers, and communicators - adhere to a set of integrity principles to protect the public's investment. Given the increasing complexity and globalization of the research enterprise, the National Academies recently re-examined and updated its integrity recommendations for researchers in the report Fostering Integrity in Research, with sponsorship from the National Science Foundation. Major departures from the previous recommendations 25-years earlier are the recognition that practices that were previously classified as merely questionable are indeed detrimental to the responsible conduct of research. Furthermore, the report concludes that there has been insufficient effort to respond to the threats that lapses in research integrity pose to the quality of research products and the reputation of researchers as deserving of the public trust. It recommends the creation of an independent, non-profit entity dedicated to promoting research integrity by serving as a resource and clearing house for expertise, advice, materials, and best practices on fostering research integrity and responding to allegations of research misconduct.
Measuring information integration
Directory of Open Access Journals (Sweden)
Sporns Olaf
2003-12-01
Full Text Available Abstract Background To understand the functioning of distributed networks such as the brain, it is important to characterize their ability to integrate information. The paper considers a measure based on effective information, a quantity capturing all causal interactions that can occur between two parts of a system. Results The capacity to integrate information, or Φ, is given by the minimum amount of effective information that can be exchanged between two complementary parts of a subset. It is shown that this measure can be used to identify the subsets of a system that can integrate information, or complexes. The analysis is applied to idealized neural systems that differ in the organization of their connections. The results indicate that Φ is maximized by having each element develop a different connection pattern with the rest of the complex (functional specialization while ensuring that a large amount of information can be exchanged across any bipartition of the network (functional integration. Conclusion Based on this analysis, the connectional organization of certain neural architectures, such as the thalamocortical system, are well suited to information integration, while that of others, such as the cerebellum, are not, with significant functional consequences. The proposed analysis of information integration should be applicable to other systems and networks.
Calhoun, Tracy; Melendrez, Dave
2014-01-01
The Human Exploration Science Office (KX) provides leadership for NASA's Imagery Integration (Integration 2) Team, an affiliation of experts in the use of engineering-class imagery intended to monitor the performance of launch vehicles and crewed spacecraft in flight. Typical engineering imagery assessments include studying and characterizing the liftoff and ascent debris environments; launch vehicle and propulsion element performance; in-flight activities; and entry, landing, and recovery operations. Integration 2 support has been provided not only for U.S. Government spaceflight (e.g., Space Shuttle, Ares I-X) but also for commercial launch providers, such as Space Exploration Technologies Corporation (SpaceX) and Orbital Sciences Corporation, servicing the International Space Station. The NASA Integration 2 Team is composed of imagery integration specialists from JSC, the Marshall Space Flight Center (MSFC), and the Kennedy Space Center (KSC), who have access to a vast pool of experience and capabilities related to program integration, deployment and management of imagery assets, imagery data management, and photogrammetric analysis. The Integration 2 team is currently providing integration services to commercial demonstration flights, Exploration Flight Test-1 (EFT-1), and the Space Launch System (SLS)-based Exploration Missions (EM)-1 and EM-2. EM-2 will be the first attempt to fly a piloted mission with the Orion spacecraft. The Integration 2 Team provides the customer (both commercial and Government) with access to a wide array of imagery options - ground-based, airborne, seaborne, or vehicle-based - that are available through the Government and commercial vendors. The team guides the customer in assembling the appropriate complement of imagery acquisition assets at the customer's facilities, minimizing costs associated with market research and the risk of purchasing inadequate assets. The NASA Integration 2 capability simplifies the process of securing one
Integrative medicine for cancer treatment
... page: //medlineplus.gov/ency/patientinstructions/000932.htm Integrative medicine for cancer treatment To use the sharing features ... This is why many people turn to integrative medicine. Integrative medicine (IM) refers to any type of ...
Integrating the Integrators - A Roadmap to Success
International Nuclear Information System (INIS)
Olson, Craig Stott; Conner, Craig C
1999-01-01
The U.S. Department of Energy Environmental Management's (DOE-EM) investments in science and technology, as well as science and technology investments associated with other parts of the DOE are aimed at meeting the Departments cleanup goals. These investments, primarily focused on EM's cleanup mission, comprise the Environmental Quality Research and Development (R and D) portfolios. Synchronizing EM's Cleanup Project Managers (operations facility and process owners throughout the DOE complex) operational needs with EM R and D including the extensive work of the six Focus Areas (major thrust areas within DOE-EM) has been a continuing challenge. This recent initiative to better integrate the R and D program is in response to evolving needs within the Department to apply proven system engineering methods to clarify requirements and define EM's process to effectively orchestrate their R and D Program. To optimize this partnership, DOE-EM's Integration Program is successfully unifying the operational needs with the R and D as described in this paper
Necessity of Integral Formalism
International Nuclear Information System (INIS)
Tao Yong
2011-01-01
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrödinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrödinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description. (general)
A Comprehensive Theory of Integration.
Singer, Sara J; Kerrissey, Michaela; Friedberg, Mark; Phillips, Russell
2018-03-01
Efforts to transform health care delivery to improve care have increasingly focused on care integration. However, variation in how integration is defined has complicated efforts to design, synthesize, and compare studies of integration in health care. Evaluations of integration initiatives would be enhanced by describing them according to clear definitions of integration and specifying which empirical relationships they seek to test-whether among types of integration or between integration and outcomes of care. Drawing on previous work, we present a comprehensive theoretical model of relationships between types of integration and propose how to measure them.
Integrated Budget Office Toolbox
Rushing, Douglas A.; Blakeley, Chris; Chapman, Gerry; Robertson, Bill; Horton, Allison; Besser, Thomas; McCarthy, Debbie
2010-01-01
The Integrated Budget Office Toolbox (IBOT) combines budgeting, resource allocation, organizational funding, and reporting features in an automated, integrated tool that provides data from a single source for Johnson Space Center (JSC) personnel. Using a common interface, concurrent users can utilize the data without compromising its integrity. IBOT tracks planning changes and updates throughout the year using both phasing and POP-related (program-operating-plan-related) budget information for the current year, and up to six years out. Separating lump-sum funds received from HQ (Headquarters) into separate labor, travel, procurement, Center G&A (general & administrative), and servicepool categories, IBOT creates a script that significantly reduces manual input time. IBOT also manages the movement of travel and procurement funds down to the organizational level and, using its integrated funds management feature, helps better track funding at lower levels. Third-party software is used to create integrated reports in IBOT that can be generated for plans, actuals, funds received, and other combinations of data that are currently maintained in the centralized format. Based on Microsoft SQL, IBOT incorporates generic budget processes, is transportable, and is economical to deploy and support.
Reconfigurable Integrated Optoelectronics
Directory of Open Access Journals (Sweden)
Richard Soref
2011-01-01
Full Text Available Integrated optics today is based upon chips of Si and InP. The future of this chip industry is probably contained in the thrust towards optoelectronic integrated circuits (OEICs and photonic integrated circuits (PICs manufactured in a high-volume foundry. We believe that reconfigurable OEICs and PICs, known as ROEICs and RPICs, constitute the ultimate embodiment of integrated photonics. This paper shows that any ROEIC-on-a-chip can be decomposed into photonic modules, some of them fixed and some of them changeable in function. Reconfiguration is provided by electrical control signals to the electro-optical building blocks. We illustrate these modules in detail and discuss 3D ROEIC chips for the highest-performance signal processing. We present examples of our module theory for RPIC optical lattice filters already constructed, and we propose new ROEICs for directed optical logic, large-scale matrix switching, and 2D beamsteering of a phased-array microwave antenna. In general, large-scale-integrated ROEICs will enable significant applications in computing, quantum computing, communications, learning, imaging, telepresence, sensing, RF/microwave photonics, information storage, cryptography, and data mining.
Fractional Integral Inequalities via Hadamard’s Fractional Integral
Sudsutad, Weerawat; Ntouyas, Sotiris K.; Tariboon, Jessada
2014-01-01
We establish new fractional integral inequalities, via Hadamard’s fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed.