Feynman amplitudes, periods and motives : international research workshop, periods and motives - a modern perspective on renormalization, July 2-6, 2012, Instituto de Ciencias Matemáticas, Madrid, Spain
著者
書誌事項
Feynman amplitudes, periods and motives : international research workshop, periods and motives - a modern perspective on renormalization, July 2-6, 2012, Instituto de Ciencias Matemáticas, Madrid, Spain
（Contemporary mathematics, 648）
American Mathematical Society, c2015
- タイトル別名
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Periods and motives
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注記
Includes bibliographical references
内容説明・目次
内容説明
This volume contains the proceedings of the International Research Workshop on Periods and Motives--A Modern Perspective on Renormalization, held from July 2-6, 2012, at the Instituto de Ciencias Matematicas, Madrid, Spain.
Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics.
Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral.
Motives emerged from Grothendieck's ``universal cohomology theory'', where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged.
The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics.
目次
A note on twistor integrals by S. Bloch
Multiple polylogarithms and linearly reducible Feynman graphs by C. Bogner and M. Luders
Comparison of motivic and simplicial operations in mod-$l$-motivic and etale cohomology by P. Brosnan and R. Joshua
On the Broadhurst-Kreimer generating series for multiple zeta values by S. Carr, H. Gangl, and L. Schneps
Dyson-Schwinger equations in the theory of computation by C. Delaney and M. Marcolli
Scattering amplitudes, Feynman integrals and multiple polylogarithms by C. Duhr
Equations D3 and spectral elliptic curves by V. Golyshev and M. Vlasenko
Quantum fields, periods and algebraic geometry by D. Kreimer
Renormalization, Hopf algebras and Mellin transforms by E. Panzer
Multiple zeta value cycles in low weight by I. Souderes
Periods and Hodge structures in perturbative quantum field theory by S. Weinzierl
Some combinatorial interpretations in perturbative quantum field theory by K. Yeats
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