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E-raamat: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions

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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 most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

This book focuses on advanced computer algebra methods and special functions that have applications in quantum field theory. It presents new methods for (infinite) multiple sums, multiple integrals, difference and differential equations.

Arvustused

From the reviews:

It is a collection of papers that grew out of a summer school course on integration, summation, and special functions in quantum field theory . if you are interested in these sorts of special functions, and the computer algebra tools to manipulate them, whether or not your particular application is quantum field theory, then this book is an excellent description of the state of the art in computer algebra manipulation and proof. (J. H. Davenport, Computing Reviews, April, 2014)

Harmonic Sums, Polylogarithms, Special Numbers, and Their Generalizations
1(32)
Jakob Ablinger
Johannes Blumlein
Multiple Zeta Values and Modular Forms in Quantum Field Theory
33(42)
David Broadhurst
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
75(22)
Stefan Gerhold
Manuel Kauers
Christoph Koutschan
Peter Paule
Carsten Schneider
Burkhard Zimmermann
Conformal Methods for Massless Feynman Integrals and Large Nf Methods
97(22)
John A. Gracey
The Holonomic Toolkit
119(26)
Manuel Kauers
Orthogonal Polynomials
145(26)
Tom H. Koornwinder
Creative Telescoping for Holonomic Functions
171(24)
Christoph Koutschan
Renormalization and Mellin Transforms
195(30)
Dirk Kreimer
Erik Panzer
Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach. I
225(18)
Peter Paule
Sergei K. Suslov
Hypergeometric Functions in Mathematica®
243(16)
Oleksandr Pavlyk
Solving Linear Recurrence Equations with Polynomial Coefficients
259(26)
Marko Petkovsek
Helena Zakrajsek
Generalization of Risch's Algorithm to Special Functions
285(20)
Clemens G. Raab
Multiple Hypergeometric Series: Appell Series and Beyond
305(20)
Michael J. Schlosser
Simplifying Multiple Sums in Difference Fields
325(36)
Carsten Schneider
Potential of FORM 4.0
361(20)
Jos A.M. Vermaseren
Feynman Graphs
381(26)
Stefan Weinzierl
Index 407