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TitleElliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory [electronic resource] / edited by Johannes Blümlein, Carsten Schneider, Peter Paule
ImprintCham : Springer International Publishing : Imprint: Springer, 2019
Edition 1st ed. 2019
Connect tohttps://doi.org/10.1007/978-3-030-04480-0
Descript XIII, 509 p. 134 illus., 54 illus. in color. online resource

SUMMARY

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.


CONTENT

Graph complexes and Cutkosky rules -- Differential equations and dispersion relations for Feynman amplitudes with elliptic functions -- Elliptic integrals and the two-loop ttbar production in QCD -- Solutions of 2nd and 3rd order differential equations with more singularities -- Analytic continuation of Feynman diagrams with elliptic solutions -- Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes -- Genus one superstring amplitudes and modular forms -- Difference field methods in Feynman diagram calculations -- Feynman integrals and iterated integrals of modular forms -- Iterated elliptic and hypergeometric integrals for Feynman diagrams. - Feynman integrals, L-series and Kloosterman moments


Algebra -- Data processing Symbolic and Algebraic Manipulation. http://scigraph.springernature.com/things/product-market-codes/I17052 Quantum Field Theories String Theory. http://scigraph.springernature.com/things/product-market-codes/P19048 Mathematical Physics. http://scigraph.springernature.com/things/product-market-codes/M35000



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