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" Elliptic integrals, elliptic functions and modular forms in quantum field theory / "
Johannes Blümlein, Carsten Schneider, Peter Paule, editors.
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BL
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| Record Number
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860344
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| Title & Author
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Elliptic integrals, elliptic functions and modular forms in quantum field theory /\ Johannes Blümlein, Carsten Schneider, Peter Paule, editors.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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Texts & monographs in symbolic computation,
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| Page. NO
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1 online resource (xiii, 509 pages) :: illustrations (some color)
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| ISBN
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3030044793
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: 3030044807
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: 3030044815
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: 9783030044794
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: 9783030044800
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: 9783030044817
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9783030044794
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| Contents
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Intro; Preface; Contents; Contributors; Eta Quotients and Rademacher Sums; 1 Introduction; 2 Eta Quotients in Quantum Field Theory; 2.1 Atkin-Lehner Transformations of Eta Quotients; 2.2 Eichler Integrals of Eta Quotients for On-Shell Sunrise Integrals; 2.3 Eichler Integrals for Quasi-periods at Level 6; 3 Rademacher Sums for Fourier Coefficients of Eta Quotients; 3.1 Genus 0; 3.2 Further Examples of Integer Sequences; 3.3 Genus 1; 3.4 Rational Rademacher Sums; 3.5 Genus 2; 3.6 Genus 3; 3.7 Genus 4; 3.8 Genus 5; 3.9 Genus 6; 3.10 Genus 7; 3.11 Genus 8; 3.12 Genus 13; 3.13 Remarks
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4 ConclusionsReferences; On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms; 1 Introduction; 2 Periodic Functions and Periods; 3 Elliptic Curves; 4 Modular Forms; 5 Iterated Integrals; 6 Precision Calculations; 7 Picard-Fuchs Operators; 8 Feynman Integrals Evaluating to Iterated Integrals of Modular Forms; 9 Conclusions; References; Iterative Non-iterative Integrals in Quantum Field Theory; 1 Introduction; 2 Second-Order Differential Equations and 2F1 Solutions; 3 Iterative Non-iterative Integrals; 4 Numerical Representation
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| Abstract
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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.
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Elliptic functions.
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Forms, Modular.
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Quantum field theory.
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Elliptic functions.
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Forms, Modular.
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Quantum field theory.
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Symbolic and Algebraic Manipulation.
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Mathematical Physics.
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Quantum Field Theories, String Theory.
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| Dewey Classification
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515/.983
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| LC Classification
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QA343
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| Added Entry
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Blümlein, J., (Johannes)
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Paule, Peter
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Schneider, Carsten
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