By Jakob Ablinger, Johannes Blümlein (auth.), Carsten Schneider, Johannes Blümlein (eds.)
The booklet specializes in complicated desktop algebra equipment and detailed features that experience extraordinary purposes within the context of quantum box conception. It provides the cutting-edge and new tools for (infinite) a number of sums, a number of integrals, specifically Feynman integrals, distinction and differential equations within the structure of survey articles. The offered recommendations emerge from interdisciplinary fields: arithmetic, laptop technological know-how and theoretical physics; the articles are written through mathematicians and physicists with the target that either teams can study from the opposite box, together with most up-to-date advancements. along with that, the gathering of articles additionally serves as an updated instruction manual of obtainable algorithms/software which are favourite or can assist within the fields of arithmetic, physics or different sciences.
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From the studies of the 1st printing of this booklet, released as quantity fifty eight of the Encyclopaedia of Mathematical Sciences:". .. This booklet could be very beneficial as a reference and consultant to researchers and graduate scholars in algebra and and topology. " Acta Scientiarum Mathematicarum, Ungarn, 1994 ". .
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Extra resources for Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions
Mod. Phys. A 15, 725–754 (2000). [hep-ph/9905237] 28. : Nested sums, expansion of transcendental functions and multiscale multiloop integrals. J. Math. Phys. 43, 3363–3386 (2002). [hep-ph/0110083] 29. : Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms. 0378 [math-ph]] 30. : Harmonic sums and polylogarithms generated by cyclotomic polynomials. J. Math. Phys. 52, 102301 (2011). 6063 [math-ph]] 31. : High precision "-expansions of massive four loop vacuum bubbles Phys.
Phys. Commun. 174, 222–240 (2006). [hep-ph/0507152] 58. : DESY 13-064 Harmonic Sums, Polylogarithms, Special Numbers, and Their Generalizations 29 59. : The theory of deeply inelastic scattering. Prog. Part. Nucl. Phys. 69, 28 (2013). 6087 [hep-ph]] 60. : Structural relations of harmonic sums and Mellin transforms at weight w D 6. , Rosenberg, S. ) Motives, Quantum Field Theory, and Pseudodifferential Operators, vol. 12, pp. 167–186. Clay Mathematics Proceedings, American Mathematical Society (2010).
Phys. Commun. 133, 76–104 (2000). : Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions. Phys. Lett. B 614, 53–61 (2005). [hep-ph/0503188] 119. : Analytic continuation of the Mellin moments of deep inelastic structure functions. [hep-ph/0501274] 120. : DESY Annual Report (2013) Multiple Zeta Values and Modular Forms in Quantum Field Theory David Broadhurst Abstract This article introduces multiple zeta values and alternating Euler sums, exposing some of the rich mathematical structure of these objects and indicating situations where they arise in quantum field theory.