Wilson Lines in Quantum Field Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin/Boston
De Gruyter
2014
|
| Schriftenreihe: | De Gruyter studies in mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Description based upon print version of record. - C.1 Basics 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 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 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 Includes bibliographical references (pages 249-251) and index |
| Beschreibung: | 1 Online-Ressource (269 p.) |
| ISBN: | 3110309106 3110309211 311030922X 3110382938 9783110309102 9783110309218 9783110309225 9783110382938 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043058618 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2014 |||| o||u| ||||||eng d | ||
| 020 | |a 3110309106 |9 3-11-030910-6 | ||
| 020 | |a 3110309211 |9 3-11-030921-1 | ||
| 020 | |a 311030922X |9 3-11-030922-X | ||
| 020 | |a 3110382938 |9 3-11-038293-8 | ||
| 020 | |a 9783110309102 |9 978-3-11-030910-2 | ||
| 020 | |a 9783110309218 |9 978-3-11-030921-8 | ||
| 020 | |a 9783110309225 |9 978-3-11-030922-5 | ||
| 020 | |a 9783110382938 |9 978-3-11-038293-8 | ||
| 035 | |a (OCoLC)897443914 | ||
| 035 | |a (DE-599)BVBBV043058618 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 530.14/35 |2 23 | |
| 100 | 1 | |a Cherednikov, Igor Olegovich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Wilson Lines in Quantum Field Theory |
| 264 | 1 | |a Berlin/Boston |b De Gruyter |c 2014 | |
| 300 | |a 1 Online-Ressource (269 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter studies in mathematical physics | |
| 500 | |a Description based upon print version of record. - C.1 Basics | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |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 | ||
| 500 | |a Includes bibliographical references (pages 249-251) and index | ||
| 650 | 7 | |a Gauge fields (Physics) |2 fast | |
| 650 | 7 | |a Loops (Group theory) |2 fast | |
| 650 | 7 | |a Quantum field theory / Mathematics |2 fast | |
| 650 | 7 | |a SCIENCE / Energy |2 bisacsh | |
| 650 | 7 | |a SCIENCE / Mechanics / General |2 bisacsh | |
| 650 | 7 | |a SCIENCE / Physics / General |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Loops (Group theory) | |
| 650 | 4 | |a Quantum field theory |x Mathematics | |
| 650 | 4 | |a Gauge fields (Physics) | |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eichtheorie |0 (DE-588)4122125-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
| 689 | 0 | 1 | |a Eichtheorie |0 (DE-588)4122125-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Mertens, Tom |e Sonstige |4 oth | |
| 700 | 1 | |a Van der Veken, Frederik F. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028482810 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175432037171200 |
|---|---|
| any_adam_object | |
| author | Cherednikov, Igor Olegovich |
| author_facet | Cherednikov, Igor Olegovich |
| author_role | aut |
| author_sort | Cherednikov, Igor Olegovich |
| author_variant | i o c io ioc |
| building | Verbundindex |
| bvnumber | BV043058618 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)897443914 (DE-599)BVBBV043058618 |
| 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 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06061nmm a2200721zc 4500</leader><controlfield tag="001">BV043058618</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2014 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110309106</subfield><subfield code="9">3-11-030910-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110309211</subfield><subfield code="9">3-11-030921-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">311030922X</subfield><subfield code="9">3-11-030922-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110382938</subfield><subfield code="9">3-11-038293-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110309102</subfield><subfield code="9">978-3-11-030910-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110309218</subfield><subfield code="9">978-3-11-030921-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110309225</subfield><subfield code="9">978-3-11-030922-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110382938</subfield><subfield code="9">978-3-11-038293-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)897443914</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043058618</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.14/35</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Cherednikov, Igor Olegovich</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Wilson Lines in Quantum Field Theory</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin/Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (269 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter studies in mathematical physics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based upon print version of record. - C.1 Basics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 249-251) and index</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Gauge fields (Physics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Loops (Group theory)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quantum field theory / Mathematics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE / Energy</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE / Mechanics / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE / Physics / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Loops (Group theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Quantum field theory</subfield><subfield code="x">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gauge fields (Physics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantenfeldtheorie</subfield><subfield code="0">(DE-588)4047984-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Eichtheorie</subfield><subfield code="0">(DE-588)4122125-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quantenfeldtheorie</subfield><subfield code="0">(DE-588)4047984-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Eichtheorie</subfield><subfield code="0">(DE-588)4122125-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mertens, Tom</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Van der Veken, Frederik F.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028482810</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043058618 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:11Z |
| institution | BVB |
| isbn | 3110309106 3110309211 311030922X 3110382938 9783110309102 9783110309218 9783110309225 9783110382938 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028482810 |
| oclc_num | 897443914 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (269 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter studies in mathematical physics |
| spelling | Cherednikov, Igor Olegovich Verfasser aut Wilson Lines in Quantum Field Theory Berlin/Boston De Gruyter 2014 1 Online-Ressource (269 p.) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematical physics Description based upon print version of record. - C.1 Basics 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 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 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 Includes bibliographical references (pages 249-251) and index Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory / Mathematics fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Mathematik Loops (Group theory) Quantum field theory Mathematics Gauge fields (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Eichtheorie (DE-588)4122125-4 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Eichtheorie (DE-588)4122125-4 s 1\p DE-604 Mertens, Tom Sonstige oth Van der Veken, Frederik F. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cherednikov, Igor Olegovich Wilson Lines in Quantum Field Theory Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory / Mathematics fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Mathematik Loops (Group theory) Quantum field theory Mathematics Gauge fields (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd Eichtheorie (DE-588)4122125-4 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4122125-4 |
| 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 |
| title_fullStr | Wilson Lines in Quantum Field Theory |
| title_full_unstemmed | Wilson Lines in Quantum Field Theory |
| title_short | Wilson Lines in Quantum Field Theory |
| title_sort | wilson lines in quantum field theory |
| topic | Gauge fields (Physics) fast Loops (Group theory) fast Quantum field theory / Mathematics fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Mathematik Loops (Group theory) Quantum field theory Mathematics Gauge fields (Physics) Quantenfeldtheorie (DE-588)4047984-5 gnd Eichtheorie (DE-588)4122125-4 gnd |
| topic_facet | Gauge fields (Physics) Loops (Group theory) Quantum field theory / Mathematics SCIENCE / Energy SCIENCE / Mechanics / General SCIENCE / Physics / General Mathematik Quantum field theory Mathematics Quantenfeldtheorie Eichtheorie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=886907 |
| work_keys_str_mv | AT cherednikovigorolegovich wilsonlinesinquantumfieldtheory AT mertenstom wilsonlinesinquantumfieldtheory AT vandervekenfrederikf wilsonlinesinquantumfieldtheory |