Overview

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. 

Full Product Details

Author:   Johannes Blümlein ,  Carsten Schneider ,  Peter Paule
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   1st ed. 2019
Weight:   0.945kg
ISBN:  

9783030044794

ISBN 10:   3030044793
Pages:   509
Publication Date:   15 February 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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.

Reviews

The book is explicitly concerned with `the mathematics of modular forms [as it is] of central importance for the analytic solution of Feynman diagrams,' but modular formers should be equally interested in the material offered in this compendium. (Michael Berg, MAA Reviews, May 19, 2019)

“The book is explicitly concerned with ‘the mathematics of modular forms [as it is] of central importance for the analytic solution of Feynman diagrams,’ but modular formers should be equally interested in the material offered in this compendium.” (Michael Berg, MAA Reviews, May 19, 2019)

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