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Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

  • Book
  • © 2019

Overview

Editors:
  1. Johannes Blümlein

    1. Deutsches Elektronen-Synchrotron, DESY, Zeuthen, Germany

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  2. Carsten Schneider

    1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  3. Peter Paule

    1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  • Presents up-to-date reviews on modular forms and functions and their use in particle physics
  • Combines knowledge from mathematical physics and mathematics
  • Written by international authors

Part of the book series: Texts & Monographs in Symbolic Computation (TEXTSMONOGR)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Eta Quotients and Rademacher Sums

    • Kevin Acres, David Broadhurst
    Pages 1-27

  3. On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms

    • Luise Adams, Stefan Weinzierl
    Pages 29-49

  4. Iterative Non-iterative Integrals in Quantum Field Theory

    • Johannes Blümlein
    Pages 51-77

  5. Analytic Continuation of the Kite Family

    • Christian Bogner, Armin Schweitzer, Stefan Weinzierl
    Pages 79-91

  6. A Four-Point Function for the Planar QCD Massive Corrections to Top-Antitop Production in the Gluon-Fusion Channel

    • Roberto Bonciani, Matteo Capozi, Paul Caucal
    Pages 93-106

  7. From Modular Forms to Differential Equations for Feynman Integrals

    • Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi
    Pages 107-131

  8. One-Loop String Scattering Amplitudes as Iterated Eisenstein Integrals

    • Johannes Broedel, Oliver Schlotterer
    Pages 133-159

  9. Expansions at Cusps and Petersson Products in Pari/GP

    • Henri Cohen
    Pages 161-181

  10. CM Evaluations of the Goswami-Sun Series

    • Madeline Locus Dawsey, Ken Ono
    Pages 183-193

  11. Automatic Proof of Theta-Function Identities

    • Jie Frye, Frank Garvan
    Pages 195-258

  12. The Generators of all Polynomial Relations Among Jacobi Theta Functions

    • Ralf Hemmecke, Cristian-Silviu Radu, Liangjie Ye
    Pages 259-268

  13. Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms

    • Fredrik Johansson
    Pages 269-293

  14. Multi-valued Feynman Graphs and Scattering Theory

    • Dirk Kreimer
    Pages 295-325

  15. Interpolated Sequences and Critical L-Values of Modular Forms

    • Robert Osburn, Armin Straub
    Pages 327-349

  16. Towards a Symbolic Summation Theory for Unspecified Sequences

    • Peter Paule, Carsten Schneider
    Pages 351-390

  17. Differential Equations and Dispersion Relations for Feynman Amplitudes

    • Ettore Remiddi
    Pages 391-414

  18. Feynman Integrals, Toric Geometry and Mirror Symmetry

    • Pierre Vanhove
    Pages 415-458

  19. Modular and Holomorphic Graph Functions from Superstring Amplitudes

    • Federico Zerbini
    Pages 459-484

  20. Some Algebraic and Arithmetic Properties of Feynman Diagrams

    • Yajun Zhou
    Pages 485-509
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Keywords

About this book

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. 

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)

Editors and Affiliations

  • Deutsches Elektronen-Synchrotron, DESY, Zeuthen, Germany

    Johannes Blümlein

  • Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Linz, Austria

    Carsten Schneider, Peter Paule

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