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The Resource Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain, Luis Álvarez-Cónsul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors

Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain, Luis Álvarez-Cónsul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors

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Summary
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
Language
eng
Work
Publication
Extent
viii, 289 pages
Contents
  • 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
Isbn
9781470422479
Instance
Label
Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain
Title
Feynman amplitudes, periods, and motives
Title remainder
international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain
Statement of responsibility
Luis Álvarez-Cónsul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors
Creator
Contributor
Editor
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
DLC
Dewey number
530.15
Illustrations
illustrations
Index
no index present
LC call number
QC20
LC item number
.F39 2015
Literary form
non fiction
http://bibfra.me/vocab/lite/meetingDate
2012
http://bibfra.me/vocab/lite/meetingName
International Research Workshop on Periods and Motives - A Modern Perspective on Renormalization
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
  • 1970-
  • 1962-
  • 1973-
http://library.link/vocab/relatedWorkOrContributorName
  • Álvarez-Cónsul, Luis
  • Burgos Gil, José I.
  • Ebrahimi-Fard, Kurusch
Series statement
Contemporary mathematics
Series volume
648
http://library.link/vocab/subjectName
  • Mathematical physics
  • Perturbation (Quantum dynamics)
  • Perturbation (Mathematics)
  • Quantum field theory
  • Number theory -- Algebraic number theory: local and $p$-adic fields -- Zeta functions and $L$-functions
  • Number theory -- Zeta and $L$-functions: analytic theory -- Multiple Dirichlet series and zeta functions and multizeta values
  • Algebraic geometry -- Cycles and subschemes -- Algebraic cycles
  • Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives
  • Algebraic geometry -- (Co)homology theory -- Motivic cohomology; motivic homotopy theory
  • Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Hopf algebras and their applications
  • Several complex variables and analytic spaces -- Deformations of analytic structures -- Period matrices, variation of Hodge structure; degenerations
  • Quantum theory -- General mathematical topics and methods in quantum theory -- Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
  • Quantum theory -- Quantum field theory; related classical field theories -- Perturbative methods of renormalization
  • Quantum theory -- Quantum field theory; related classical field theories -- Feynman diagrams
  • Mathematical physics
  • Perturbation (Mathematics)
  • Perturbation (Quantum dynamics)
  • Quantum field theory
Label
Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain, Luis Álvarez-Cónsul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
907132659
Dimensions
26 cm
Extent
viii, 289 pages
Isbn
9781470422479
Isbn Type
(alk. paper)
Lccn
2015010413
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Specific material designation
regular print
System control number
(OCoLC)907132659
Label
Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matemáticas, Madrid, Spain, Luis Álvarez-Cónsul, Jose Ignacio Burgos-Gil, Kurusch Ebrahimi-Fard, editors
Publication
Copyright
Bibliography note
Includes bibliographical references
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
907132659
Dimensions
26 cm
Extent
viii, 289 pages
Isbn
9781470422479
Isbn Type
(alk. paper)
Lccn
2015010413
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Specific material designation
regular print
System control number
(OCoLC)907132659

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