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Dyson Schwinger Equations Renormalization Conditions And The Hopf Algebra Of Perturbative Quantum Field Theory

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Dyson Schwinger Equations Renormalization Conditions And The Hopf Algebra Of Perturbative Quantum Field Theory

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Author : Paul-Hermann Balduf
language : en
Publisher: Springer Nature
Release Date : 2024-04-26

Dyson Schwinger Equations Renormalization Conditions And The Hopf Algebra Of Perturbative Quantum Field Theory written by Paul-Hermann Balduf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Science categories.

This book offers a systematic introduction to the Hopf algebra of renormalization in quantum field theory, with a special focus on physical motivation, the role of Dyson–Schwinger equations, and the renormalization group. All necessary physical and mathematical constructions are reviewed and motivated in a self-contained introduction. The main part of the book concerns the interplay between Dyson–Schwinger equations (DSEs) and renormalization conditions. The book is explicit and consistent about whether a statement is true in general or only in particular renormalization schemes or approximations and about the dependence of quantities on regularization parameters or coupling constants. With over 600 references, the original literature is cited whenever possible and the book contains numerous references to other works discussing further details, generalizations, or alternative approaches. There are explicit examples and remarks to make the connection from the scalar fields at hand toQED and QCD. The book is primarily targeted at the mathematically oriented physicist who seeks a systematic conceptual overview of renormalization, Hopf algebra, and DSEs. These may be graduate students entering the field as well as practitioners seeking a self-contained account of the Hopf algebra construction. Conversely, the book also benefits the mathematician who is interested in the physical background of the exciting interplay between Hopf algebra, combinatorics and physics that is renormalization theory today.

Quantum Field Theory

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Author : Bertfried Fauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-02

Quantum Field Theory written by Bertfried Fauser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-02 with Science categories.

The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

Arithmetic And Geometry Around Quantization

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Author : Özgür Ceyhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-12

Arithmetic And Geometry Around Quantization written by Özgür Ceyhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-12 with Mathematics categories.

This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.

Clifford Algebras And Their Applications In Mathematical Physics

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Author : Rafał Abłamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

Clifford Algebras And Their Applications In Mathematical Physics written by Rafał Abłamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

Clifford Algebras And Their Applications In Mathematical Physics

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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Clifford Algebras And Their Applications In Mathematical Physics written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.

Clifford Algebras And Their Applications In Mathematical Physics

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Author : John Ryan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Clifford Algebras And Their Applications In Mathematical Physics written by John Ryan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Feynman Amplitudes Periods And Motives

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Author : Luis Álvarez-Cónsul
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-24

Feynman Amplitudes Periods And Motives written by Luis Álvarez-Cónsul and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.

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.