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Computer Algebra in Quantum Field Theory : Integration, Summation and Special Functions / edited by Carsten Schneider, Johannes Blümlein.
- Format:
- Book
- Series:
- Computer Science (Springer-11645)
- Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,. 0943-853X
- Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 0943-853X
- Language:
- English
- Subjects (All):
- Particles (Nuclear physics).
- Quantum field theory.
- Mathematical physics.
- String models.
- Functions, Special.
- Computer science--Mathematics.
- Computer science.
- Elementary Particles, Quantum Field Theory.
- Mathematical Physics.
- Quantum Field Theories, String Theory.
- Special Functions.
- Symbolic and Algebraic Manipulation.
- Local Subjects:
- Elementary Particles, Quantum Field Theory.
- Mathematical Physics.
- Quantum Field Theories, String Theory.
- Special Functions.
- Symbolic and Algebraic Manipulation.
- Physical Description:
- 1 online resource (XIV, 411 pages) : 41 illustrations.
- Edition:
- First edition 2013.
- Contained In:
- Springer eBooks
- Place of Publication:
- Vienna : Springer Vienna : Imprint: Springer, 2013.
- System Details:
- text file PDF
- Summary:
- 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.
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-7091-1616-6
- 9783709116166
- Access Restriction:
- Restricted for use by site license.
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