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Author International Research Workshop Periods and Motives - a Modern Perspective on Renormalization (2012 : Madrid, Spain)
Title 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 / Luis Álvarez-Cónsul, José Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors
Imprint Providence, Rhode Island : American Mathematical Society, [2015]
book jacket
 Mathematics Library  QC20 I58 2012    AVAILABLE    30340200545253
Descript viii, 289 pages : illustrations ; 26 cm
Series Contemporary mathematics ; 648
Contemporary mathematics (American Mathematical Society) ; v. 648
Note Includes bibliographical references
A note on twistor integrals -- Multiple polylogarithms and linearly reducible Feynman graphs -- Comparison of motivic and simplicial operations in mod-l-motivic and étale cohomology -- On the Broadhurst-Kreimer generating series for multiple zeta values -- Dyson-Schwinger equations in the theory of computation -- Scattering amplitudes, Feynman integrals and multiple polylogarithms -- Equations D3 and spectral elliptic curves -- Quantum fields, periods and algebraic geometry -- Renormalization, Hopf algebras and Mellin transforms -- Multiple zeta value cycles in low weight -- Periods and Hodge structures in perturbative quantum field theory -- Some combinatorial interpretations in perturbative quantum field theory
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 Matemáticas, 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
Subject Mathematical physics -- Congresses
Perturbation (Quantum dynamics) -- Congresses
Perturbation (Mathematics) -- Congresses
Quantum field theory -- Congresses
Number theory -- Algebraic number theory: local and $p$-adic fields -- Zeta functions and $L$-functions. msc
Number theory -- Zeta and $L$-functions: analytic theory -- Multiple Dirichlet series and zeta functions and multizeta values. msc
Algebraic geometry -- Cycles and subschemes -- Algebraic cycles. msc
Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives. msc
Algebraic geometry -- (Co)homology theory -- Motivic cohomology; motivic homotopy theory. msc
Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Hopf algebras and their applications. msc
Several complex variables and analytic spaces -- Deformations of analytic structures -- Period matrices, variation of Hodge structure; degenerations. msc
Quantum theory -- General mathematical topics and methods in quantum theory -- Feynman integrals and graphs; applications of algebraic topology and algebraic geometry. msc
Quantum theory -- Quantum field theory; related classical field theories -- Perturbative methods of renormalization. msc
Quantum theory -- Quantum field theory; related classical field theories -- Feynman diagrams. msc
Alt Author Álvarez-Cónsul, Luis, 1970- editor
Burgos Gil, José I. (José Ignacio), 1962- editor
Ebrahimi-Fard, Kurusch, 1973- editor
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