Computer Algebra in Quantum Field Theory Integration, Summation and Special Functions /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Schneider, Carsten. (Editor), Bl<U+00fc>mlein, Johannes. (Editor)
• Format: Electronic
• Language: English
• Published: Vienna : Springer Vienna : Imprint: Springer, 2013.
• Series: Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
• Subjects: Physics.; Algebra > Data processing.; Functions, special.; Quantum theory.; Elementary Particles, Quantum Field Theory.; Mathematical Physics.; Quantum Field Theories, String Theory.; Special Functions.; Symbolic and Algebraic Manipulation.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-7091-1616-6

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 diffe...

Table of Contents:

• Harmonic sums, polylogarithms, special numbers, and their generalizations
• Multiple Zeta values and modular forms in quantum field theory
• Computer-assisted proofs of some identities for Bessel functions of fractional order
• Conformal methods for massless Feynman integrals and large Nf methods
• The holonomic toolkit
• Orthogonal polynomials
• Creative telescoping for holonomic functions
• Renormalization and Mellin transforms
• Relativistic Coulomb integrals and Zeilberger's holonomic systems approach
• Hypergeometric functions in Mathematica
• Solving linear recurrence equations with polynomial coefficients
• Generalization of Risch's algorithms to special functions
• Multiple hypergeometric series
• Appell series and beyond
• Simplifying multiple sums in difference fields
• Potential of FORM 4.0
• Feynman graphs.