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OverviewThis 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. Full Product DetailsAuthor: Luis Alvarez-Consul , Jose Ignacio Burgos-Gil , Kurusch Ebrahimi-FardPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.280kg ISBN: 9781470422479ISBN 10: 1470422476 Pages: 289 Publication Date: 30 October 2015 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsA 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. YeatsReviewsAuthor InformationLuis Alvarez-Consul, Jose Ignacio Burgos-Gil, and Kurusch Ebrahimi-Fard, Instituto de Ciencias Matematicas, Madrid, Spain. Tab Content 6Author Website:Countries AvailableAll regions |
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