Elliptic integrals, elliptic functions and modular forms in quantum field theory /
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| Imprint: | Cham, Switzerland : Springer, 2019. |
|---|---|
| Description: | 1 online resource (xiii, 509 pages) : illustrations (some color) |
| Language: | English |
| Series: | Texts & monographs in symbolic computation, 0943-853X Texts and monographs in symbolic computation, |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11781523 |
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| 245 | 0 | 0 | |a Elliptic integrals, elliptic functions and modular forms in quantum field theory / |c Johannes Blümlein, Carsten Schneider, Peter Paule, editors. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c 2019. | |
| 300 | |a 1 online resource (xiii, 509 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Texts & monographs in symbolic computation, |x 0943-853X | |
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed February 7, 2019). | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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. | ||
| 650 | 0 | |a Elliptic functions. |0 http://id.loc.gov/authorities/subjects/sh85052336 | |
| 650 | 0 | |a Forms, Modular. |0 http://id.loc.gov/authorities/subjects/sh85050826 | |
| 650 | 0 | |a Quantum field theory. |0 http://id.loc.gov/authorities/subjects/sh85109461 | |
| 650 | 1 | 4 | |a Symbolic and Algebraic Manipulation. |0 http://scigraph.springernature.com/things/product-market-codes/I17052 |
| 650 | 2 | 4 | |a Quantum Field Theories, String Theory. |0 http://scigraph.springernature.com/things/product-market-codes/P19048 |
| 650 | 2 | 4 | |a Mathematical Physics. |0 http://scigraph.springernature.com/things/product-market-codes/M35000 |
| 650 | 7 | |a Elliptic functions. |2 fast |0 (OCoLC)fst00908173 | |
| 650 | 7 | |a Forms, Modular. |2 fast |0 (OCoLC)fst00932983 | |
| 650 | 7 | |a Quantum field theory. |2 fast |0 (OCoLC)fst01085105 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Blümlein, J. |q (Johannes), |e editor. |0 http://id.loc.gov/authorities/names/n93032457 | |
| 700 | 1 | |a Schneider, Carsten, |e editor. | |
| 700 | 1 | |a Paule, Peter, |e editor. |0 http://id.loc.gov/authorities/names/nb2011000006 | |
| 776 | 0 | 8 | |i Printed edition: |z 9783030044794 |
| 776 | 0 | 8 | |i Printed edition: |z 9783030044817 |
| 830 | 0 | |a Texts and monographs in symbolic computation, |x 0943-853X |0 http://id.loc.gov/authorities/names/n93061753 | |
| 880 | 8 | |6 505-00/(S |a 4 Some Examples and Applications4.1 Elliptic Multiple Zeta Values as Iterated Integrals Over Modular Forms for Γ(2); 4.2 A Canonical Differential Equation for Some Classes of Hypergeometric Functions; 4.3 Modular Forms for Γ1(6) and the Sunrise and the Kite Integrals; 5 Conclusions and Outlook; References; One-Loop String Scattering Amplitudes as Iterated Eisenstein Integrals; 1 Introduction; 2 One-Loop Open-String Amplitudes, Planar and Non-planar; 2.1 General Setup, Planar and Non-planar; 2.2 Four-Point Amplitudes; 2.3 Five-Point Amplitudes; 2.4 Higher-Point Amplitudes | |
| 880 | 8 | |6 505-00/(S |a 5 Representation in Terms of Modular Forms5.1 The Mathematical Framework; 5.2 The q-Representation of the Inhomogeneous Solution; 6 The ρ-Parameter; 7 Conclusions; References; Analytic Continuation of the Kite Family; 1 Introduction; 2 The Kite Family and Its Elliptic Curve; 3 Analytic Continuation; 4 An Application of the Picard-Lefschetz Formula; References; A Four-Point Function for the Planar QCD Massive Corrections to Top-Antitop Production in the Gluon-Fusion Channel; 1 Introduction; 2 Notations; 3 The Differential Equations; 3.1 Second Order Differential Equation | |
| 880 | 8 | |6 505-00/(S |a 3.2 Homogeneous Solution and Maximal Cut3.3 Complete Solution; 3.4 The MIs mathcalT33 and mathcalT35; 4 Conclusions; References; From Modular Forms to Differential Equations for Feynman Integrals; 1 Introduction; 2 Terms and Definitions; 2.1 The Modular Group SL(2,mathbbZ) and Its Congruence Subgroups; 2.2 Modular Curves; 2.3 Modular Forms; 3 An Algebraic Representation of Modular Forms; 3.1 General Considerations; 3.2 A Basis for Modular Forms for Γ(2); 3.3 A Basis for Modular Forms for Γ0(2); 3.4 A Basis for Modular Forms for Γ0(4) and Γ0(6); 3.5 A Basis for Modular Forms for Γ1(6) | |
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