Wilson Lines in Quantum Field Theory /:
The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. Itteaches how to perform independently with some elementary calculationson Wilson lines, and shows the recent develop...
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Berlin ; München ; Boston :
DE GRUYTER,
2014.
|
Ausgabe: | 2014. |
Schriftenreihe: | De Gruyter studies in mathematical physics.
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Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. Itteaches how to perform independently with some elementary calculationson Wilson lines, and shows the recent development of the subject in different important areas of research. |
Beschreibung: | 1 online resource |
Bibliographie: | Includes bibliographical references (pages 249-251) and index. |
ISBN: | 9783110309218 3110309211 9783110382938 3110382938 9783110651690 3110651696 |
Internformat
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245 | 1 | 0 | |a Wilson Lines in Quantum Field Theory / |c Igor Olegovich Cherednikov, Tom Mertens, Frederik F. Van der Veken. |
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490 | 1 | |a De Gruyter Studies in Mathematical Physics ; |v v. 24 | |
504 | |a Includes bibliographical references (pages 249-251) and index. | ||
505 | 0 | |a Preface; 1 Introduction: What are Wilson lines?; 2 Prolegomena to the mathematical theory of Wilson lines; 2.1 Shuffle algebra and the idea of algebraic paths; 2.1.1 Shuffle algebra: Definition and properties; 2.1.2 Chen's algebraic paths; 2.1.3 Chen iterated integrals; 2.2 Gauge fields as connections on a principal bundle; 2.2.1 Principal fiber bundle, sections and associated vector bundle; 2.2.2 Gauge field as a connection; 2.2.3 Horizontal lift and parallel transport; 2.3 Solving matrix differential equations: Chen iterated integrals; 2.3.1 Derivatives of a matrix function. | |
505 | 8 | |6 880-01 |a 3.4 The group of generalized loops3.5 Generalized loops and the Ambrose-Singer theorem; 3.6 The Lie algebra of the group of the generalized loops; 4 Shape variations in the loop space; 4.1 Path derivatives; 4.2 Area derivative; 4.3 Variational calculus; 4.4 Fréchet derivative in a generalized loop space; 5 Wilson lines in high-energy QCD; 5.1 Eikonal approximation; 5.1.1 Wilson line on a linear path; 5.1.2 Wilson line as an eikonal line; 5.2 Deep inelastic scattering; 5.2.1 Kinematics; 5.2.2 Invitation: the free parton model; 5.2.3 A more formal approach; 5.2.4 Parton distribution functions. | |
505 | 8 | |a 5.2.5 Operator definition for PDFs5.2.6 Gauge invariant operator definition; 5.2.7 Collinear factorization and evolution of PDFs; 5.3 Semi-inclusive deep inelastic scattering; 5.3.1 Conventions and kinematics; 5.3.2 Structure functions; 5.3.3 Transverse momentum dependent PDFs; 5.3.4 Gauge-invariant definition for TMDs; A Mathematical vocabulary; A.1 General topology; A.2 Topology and basis; A.3 Continuity; A.4 Connectedness; A.5 Local connectedness and local path-connectedness; A.6 Compactness; A.7 Countability axioms and Baire theorem; A.8 Convergence; A.9 Separation properties. | |
505 | 8 | |a A.10 Local compactness and compactificationA. 11 Quotient topology; A.12 Fundamental group; A.13 Manifolds; A.14 Differential calculus; A.15 Stokes' theorem; A.16 Algebra: Rings and modules; A.17 Algebra: Ideals; A.18 Algebras; A.19 Hopf algebra; A.20 Topological, C*-, and Banach algebras; A.21 Nuclear multiplicative convex Hausdorff algebras and the Gel'fand spectrum; B Notations and conventions in quantum field theory; B.1 Vectors and tensors; B.2 Spinors and gamma matrices; B.3 Light-cone coordinates; B.4 Fourier transforms and distributions; B.5 Feynman rules for QCD; C Color algebra. | |
520 | |a The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. Itteaches how to perform independently with some elementary calculationson Wilson lines, and shows the recent development of the subject in different important areas of research. | ||
650 | 0 | |a Loops (Group theory) |0 http://id.loc.gov/authorities/subjects/sh85078321 | |
650 | 0 | |a Quantum field theory |x Mathematics. | |
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880 | 8 | |6 505-01/(S |a 2.3.2 Product integral of a matrix function2.3.3 Continuity of matrix functions; 2.3.4 Iterated integrals and path ordering; 2.4 Wilson lines, parallel transport and covariant derivative; 2.4.1 Parallel transport and Wilson lines; 2.4.2 Holonomy, curvature and the Ambrose-Singer theorem; 2.5 Generalization of manifolds and derivatives; 2.5.1 Manifold: Fréchet derivative and Banach manifold; 2.5.2 Fréchet manifold; 3 The group of generalized loops and its Lie algebra; 3.1 Introduction; 3.2 The shuffle algebra over Ω = ∧M as a Hopf algebra; 3.3 The group of loops. | |
880 | |6 500-00/(S |a 2.3.2 Product integral of a matrix function2.3.3 Continuity of matrix functions; 2.3.4 Iterated integrals and path ordering; 2.4 Wilson lines, parallel transport and covariant derivative; 2.4.1 Parallel transport and Wilson lines; 2.4.2 Holonomy, curvature and the Ambrose-Singer theorem; 2.5 Generalization of manifolds and derivatives; 2.5.1 Manifold: Fréchet derivative and Banach manifold; 2.5.2 Fréchet manifold; 3 The group of generalized loops and its Lie algebra; 3.1 Introduction; 3.2 The shuffle algebra over Ω = ∧M as a Hopf algebra; 3.3 The group of loops. | ||
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Datensatz im Suchindex
DE-BY-FWS_katkey | ZDB-4-EBA-ocn897443914 |
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adam_text | |
any_adam_object | |
author | Cherednikov, Igor Olegovich |
author2 | Mertens, Tom Veken, Frederik F. Van der |
author2_role | |
author2_variant | t m tm f f v d v ffvd ffvdv |
author_facet | Cherednikov, Igor Olegovich Mertens, Tom Veken, Frederik F. Van der |
author_role | |
author_sort | Cherednikov, Igor Olegovich |
author_variant | i o c io ioc |
building | Verbundindex |
bvnumber | localFWS |
callnumber-first | Q - Science |
callnumber-label | QA174 |
callnumber-raw | QA174.2 .C45 2014 |
callnumber-search | QA174.2 .C45 2014 |
callnumber-sort | QA 3174.2 C45 42014 |
callnumber-subject | QA - Mathematics |
collection | ZDB-4-EBA |
contents | Preface; 1 Introduction: What are Wilson lines?; 2 Prolegomena to the mathematical theory of Wilson lines; 2.1 Shuffle algebra and the idea of algebraic paths; 2.1.1 Shuffle algebra: Definition and properties; 2.1.2 Chen's algebraic paths; 2.1.3 Chen iterated integrals; 2.2 Gauge fields as connections on a principal bundle; 2.2.1 Principal fiber bundle, sections and associated vector bundle; 2.2.2 Gauge field as a connection; 2.2.3 Horizontal lift and parallel transport; 2.3 Solving matrix differential equations: Chen iterated integrals; 2.3.1 Derivatives of a matrix function. 3.4 The group of generalized loops3.5 Generalized loops and the Ambrose-Singer theorem; 3.6 The Lie algebra of the group of the generalized loops; 4 Shape variations in the loop space; 4.1 Path derivatives; 4.2 Area derivative; 4.3 Variational calculus; 4.4 Fréchet derivative in a generalized loop space; 5 Wilson lines in high-energy QCD; 5.1 Eikonal approximation; 5.1.1 Wilson line on a linear path; 5.1.2 Wilson line as an eikonal line; 5.2 Deep inelastic scattering; 5.2.1 Kinematics; 5.2.2 Invitation: the free parton model; 5.2.3 A more formal approach; 5.2.4 Parton distribution functions. 5.2.5 Operator definition for PDFs5.2.6 Gauge invariant operator definition; 5.2.7 Collinear factorization and evolution of PDFs; 5.3 Semi-inclusive deep inelastic scattering; 5.3.1 Conventions and kinematics; 5.3.2 Structure functions; 5.3.3 Transverse momentum dependent PDFs; 5.3.4 Gauge-invariant definition for TMDs; A Mathematical vocabulary; A.1 General topology; A.2 Topology and basis; A.3 Continuity; A.4 Connectedness; A.5 Local connectedness and local path-connectedness; A.6 Compactness; A.7 Countability axioms and Baire theorem; A.8 Convergence; A.9 Separation properties. A.10 Local compactness and compactificationA. 11 Quotient topology; A.12 Fundamental group; A.13 Manifolds; A.14 Differential calculus; A.15 Stokes' theorem; A.16 Algebra: Rings and modules; A.17 Algebra: Ideals; A.18 Algebras; A.19 Hopf algebra; A.20 Topological, C*-, and Banach algebras; A.21 Nuclear multiplicative convex Hausdorff algebras and the Gel'fand spectrum; B Notations and conventions in quantum field theory; B.1 Vectors and tensors; B.2 Spinors and gamma matrices; B.3 Light-cone coordinates; B.4 Fourier transforms and distributions; B.5 Feynman rules for QCD; C Color algebra. |
ctrlnum | (OCoLC)897443914 |
dewey-full | 530.14/35 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 530 - Physics |
dewey-raw | 530.14/35 |
dewey-search | 530.14/35 |
dewey-sort | 3530.14 235 |
dewey-tens | 530 - Physics |
discipline | Physik |
edition | 2014. |
format | Electronic eBook |
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id | ZDB-4-EBA-ocn897443914 |
illustrated | Not Illustrated |
indexdate | 2024-11-27T13:26:21Z |
institution | BVB |
isbn | 9783110309218 3110309211 9783110382938 3110382938 9783110651690 3110651696 |
language | English |
oclc_num | 897443914 |
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owner | MAIN DE-863 DE-BY-FWS |
owner_facet | MAIN DE-863 DE-BY-FWS |
physical | 1 online resource |
psigel | ZDB-4-EBA |
publishDate | 2014 |
publishDateSearch | 2014 |
publishDateSort | 2014 |
publisher | DE GRUYTER, |
record_format | marc |
series | De Gruyter studies in mathematical physics. |
series2 | De Gruyter Studies in Mathematical Physics ; |
spelling | Cherednikov, Igor Olegovich. Wilson Lines in Quantum Field Theory / Igor Olegovich Cherednikov, Tom Mertens, Frederik F. Van der Veken. 2014. Berlin ; München ; Boston : DE GRUYTER, 2014. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Studies in Mathematical Physics ; v. 24 Includes bibliographical references (pages 249-251) and index. Preface; 1 Introduction: What are Wilson lines?; 2 Prolegomena to the mathematical theory of Wilson lines; 2.1 Shuffle algebra and the idea of algebraic paths; 2.1.1 Shuffle algebra: Definition and properties; 2.1.2 Chen's algebraic paths; 2.1.3 Chen iterated integrals; 2.2 Gauge fields as connections on a principal bundle; 2.2.1 Principal fiber bundle, sections and associated vector bundle; 2.2.2 Gauge field as a connection; 2.2.3 Horizontal lift and parallel transport; 2.3 Solving matrix differential equations: Chen iterated integrals; 2.3.1 Derivatives of a matrix function. 880-01 3.4 The group of generalized loops3.5 Generalized loops and the Ambrose-Singer theorem; 3.6 The Lie algebra of the group of the generalized loops; 4 Shape variations in the loop space; 4.1 Path derivatives; 4.2 Area derivative; 4.3 Variational calculus; 4.4 Fréchet derivative in a generalized loop space; 5 Wilson lines in high-energy QCD; 5.1 Eikonal approximation; 5.1.1 Wilson line on a linear path; 5.1.2 Wilson line as an eikonal line; 5.2 Deep inelastic scattering; 5.2.1 Kinematics; 5.2.2 Invitation: the free parton model; 5.2.3 A more formal approach; 5.2.4 Parton distribution functions. 5.2.5 Operator definition for PDFs5.2.6 Gauge invariant operator definition; 5.2.7 Collinear factorization and evolution of PDFs; 5.3 Semi-inclusive deep inelastic scattering; 5.3.1 Conventions and kinematics; 5.3.2 Structure functions; 5.3.3 Transverse momentum dependent PDFs; 5.3.4 Gauge-invariant definition for TMDs; A Mathematical vocabulary; A.1 General topology; A.2 Topology and basis; A.3 Continuity; A.4 Connectedness; A.5 Local connectedness and local path-connectedness; A.6 Compactness; A.7 Countability axioms and Baire theorem; A.8 Convergence; A.9 Separation properties. A.10 Local compactness and compactificationA. 11 Quotient topology; A.12 Fundamental group; A.13 Manifolds; A.14 Differential calculus; A.15 Stokes' theorem; A.16 Algebra: Rings and modules; A.17 Algebra: Ideals; A.18 Algebras; A.19 Hopf algebra; A.20 Topological, C*-, and Banach algebras; A.21 Nuclear multiplicative convex Hausdorff algebras and the Gel'fand spectrum; B Notations and conventions in quantum field theory; B.1 Vectors and tensors; B.2 Spinors and gamma matrices; B.3 Light-cone coordinates; B.4 Fourier transforms and distributions; B.5 Feynman rules for QCD; C Color algebra. The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. Itteaches how to perform independently with some elementary calculationson Wilson lines, and shows the recent development of the subject in different important areas of research. Loops (Group theory) http://id.loc.gov/authorities/subjects/sh85078321 Quantum field theory Mathematics. Gauge fields (Physics) http://id.loc.gov/authorities/subjects/sh85053534 Lacets (Théorie des groupes) Théorie quantique des champs Mathématiques. Champs de jauge (Physique) SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory Mathematics fast Mertens, Tom. Veken, Frederik F. Van der. Print 9783110309102 De Gruyter studies in mathematical physics. http://id.loc.gov/authorities/names/no2012028823 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886907 Volltext 505-01/(S 2.3.2 Product integral of a matrix function2.3.3 Continuity of matrix functions; 2.3.4 Iterated integrals and path ordering; 2.4 Wilson lines, parallel transport and covariant derivative; 2.4.1 Parallel transport and Wilson lines; 2.4.2 Holonomy, curvature and the Ambrose-Singer theorem; 2.5 Generalization of manifolds and derivatives; 2.5.1 Manifold: Fréchet derivative and Banach manifold; 2.5.2 Fréchet manifold; 3 The group of generalized loops and its Lie algebra; 3.1 Introduction; 3.2 The shuffle algebra over Ω = ∧M as a Hopf algebra; 3.3 The group of loops. 500-00/(S 2.3.2 Product integral of a matrix function2.3.3 Continuity of matrix functions; 2.3.4 Iterated integrals and path ordering; 2.4 Wilson lines, parallel transport and covariant derivative; 2.4.1 Parallel transport and Wilson lines; 2.4.2 Holonomy, curvature and the Ambrose-Singer theorem; 2.5 Generalization of manifolds and derivatives; 2.5.1 Manifold: Fréchet derivative and Banach manifold; 2.5.2 Fréchet manifold; 3 The group of generalized loops and its Lie algebra; 3.1 Introduction; 3.2 The shuffle algebra over Ω = ∧M as a Hopf algebra; 3.3 The group of loops. |
spellingShingle | Cherednikov, Igor Olegovich Wilson Lines in Quantum Field Theory / De Gruyter studies in mathematical physics. Preface; 1 Introduction: What are Wilson lines?; 2 Prolegomena to the mathematical theory of Wilson lines; 2.1 Shuffle algebra and the idea of algebraic paths; 2.1.1 Shuffle algebra: Definition and properties; 2.1.2 Chen's algebraic paths; 2.1.3 Chen iterated integrals; 2.2 Gauge fields as connections on a principal bundle; 2.2.1 Principal fiber bundle, sections and associated vector bundle; 2.2.2 Gauge field as a connection; 2.2.3 Horizontal lift and parallel transport; 2.3 Solving matrix differential equations: Chen iterated integrals; 2.3.1 Derivatives of a matrix function. 3.4 The group of generalized loops3.5 Generalized loops and the Ambrose-Singer theorem; 3.6 The Lie algebra of the group of the generalized loops; 4 Shape variations in the loop space; 4.1 Path derivatives; 4.2 Area derivative; 4.3 Variational calculus; 4.4 Fréchet derivative in a generalized loop space; 5 Wilson lines in high-energy QCD; 5.1 Eikonal approximation; 5.1.1 Wilson line on a linear path; 5.1.2 Wilson line as an eikonal line; 5.2 Deep inelastic scattering; 5.2.1 Kinematics; 5.2.2 Invitation: the free parton model; 5.2.3 A more formal approach; 5.2.4 Parton distribution functions. 5.2.5 Operator definition for PDFs5.2.6 Gauge invariant operator definition; 5.2.7 Collinear factorization and evolution of PDFs; 5.3 Semi-inclusive deep inelastic scattering; 5.3.1 Conventions and kinematics; 5.3.2 Structure functions; 5.3.3 Transverse momentum dependent PDFs; 5.3.4 Gauge-invariant definition for TMDs; A Mathematical vocabulary; A.1 General topology; A.2 Topology and basis; A.3 Continuity; A.4 Connectedness; A.5 Local connectedness and local path-connectedness; A.6 Compactness; A.7 Countability axioms and Baire theorem; A.8 Convergence; A.9 Separation properties. A.10 Local compactness and compactificationA. 11 Quotient topology; A.12 Fundamental group; A.13 Manifolds; A.14 Differential calculus; A.15 Stokes' theorem; A.16 Algebra: Rings and modules; A.17 Algebra: Ideals; A.18 Algebras; A.19 Hopf algebra; A.20 Topological, C*-, and Banach algebras; A.21 Nuclear multiplicative convex Hausdorff algebras and the Gel'fand spectrum; B Notations and conventions in quantum field theory; B.1 Vectors and tensors; B.2 Spinors and gamma matrices; B.3 Light-cone coordinates; B.4 Fourier transforms and distributions; B.5 Feynman rules for QCD; C Color algebra. Loops (Group theory) http://id.loc.gov/authorities/subjects/sh85078321 Quantum field theory Mathematics. Gauge fields (Physics) http://id.loc.gov/authorities/subjects/sh85053534 Lacets (Théorie des groupes) Théorie quantique des champs Mathématiques. Champs de jauge (Physique) SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory Mathematics fast |
subject_GND | http://id.loc.gov/authorities/subjects/sh85078321 http://id.loc.gov/authorities/subjects/sh85053534 |
title | Wilson Lines in Quantum Field Theory / |
title_auth | Wilson Lines in Quantum Field Theory / |
title_exact_search | Wilson Lines in Quantum Field Theory / |
title_full | Wilson Lines in Quantum Field Theory / Igor Olegovich Cherednikov, Tom Mertens, Frederik F. Van der Veken. |
title_fullStr | Wilson Lines in Quantum Field Theory / Igor Olegovich Cherednikov, Tom Mertens, Frederik F. Van der Veken. |
title_full_unstemmed | Wilson Lines in Quantum Field Theory / Igor Olegovich Cherednikov, Tom Mertens, Frederik F. Van der Veken. |
title_short | Wilson Lines in Quantum Field Theory / |
title_sort | wilson lines in quantum field theory |
topic | Loops (Group theory) http://id.loc.gov/authorities/subjects/sh85078321 Quantum field theory Mathematics. Gauge fields (Physics) http://id.loc.gov/authorities/subjects/sh85053534 Lacets (Théorie des groupes) Théorie quantique des champs Mathématiques. Champs de jauge (Physique) SCIENCE Energy. bisacsh SCIENCE Mechanics General. bisacsh SCIENCE Physics General. bisacsh Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory Mathematics fast |
topic_facet | Loops (Group theory) Quantum field theory Mathematics. Gauge fields (Physics) Lacets (Théorie des groupes) Théorie quantique des champs Mathématiques. Champs de jauge (Physique) SCIENCE Energy. SCIENCE Mechanics General. SCIENCE Physics General. Quantum field theory Mathematics |
url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=886907 |
work_keys_str_mv | AT cherednikovigorolegovich wilsonlinesinquantumfieldtheory AT mertenstom wilsonlinesinquantumfieldtheory AT vekenfrederikfvander wilsonlinesinquantumfieldtheory |