Wilson lines in quantum field theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2014
|
| Series: | De Gruyter studies in mathematical physics
24 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XI, 257 S. graph. Darst. 240 mm x 170 mm |
| ISBN: | 3110309106 9783110309102 |
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MARC
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Record in the Search Index
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CONTENTS
PREFACE V
1 INTRODUCTION: WHAT ARE WILSON LINES? 1
2 PROLEGOMENA TO THE MATHEMATICAL THEORY OF WILSON LINES 6
2.1 SHUFFLE ALGEBRA AND THE IDEA OF ALGEBRAIC PATHS 7
2.1.1 SHUFFLE ALGEBRA: DEFINITION AND PROPERTIES 7
2.1.2 CHEN'S ALGEBRAIC PATHS 21
2.1.3 CHEN ITERATED INTEGRALS 39
2.2 GAUGE FIELDS AS CONNECTIONS ON A PRINCIPAL BUNDLE 44
2.2.1 PRINCIPAL FIBER BUNDLE, SECTIONS AND ASSOCIATED VECTOR BUNDLE 45
2.2.2 GAUGE FIELD AS A CONNECTION 50
2.2.3 HORIZONTAL LIFT AND PARALLEL TRANSPORT 55
2.3 SOLVING MATRIX DIFFERENTIAL EQUATIONS: CHEN ITERATED INTEGRALS 56
2.3.1 DERIVATIVES OF A MATRIX FUNCTION 57
2.3.2 PRODUCT INTEGRAL OF A MATRIX FUNCTION 59
2.3.3 CONTINUITY OF MATRIX FUNCTIONS 61
2.3.4 ITERATED INTEGRALS AND PATH ORDERING 63
2.4 WILSON LINES, PARALLEL TRANSPORT AND COVARIANT DERIVATIVE 65
2.4.1 PARALLEL TRANSPORT AND WILSON LINES 65
2.4.2 HOLONOMY, CURVATURE AND THE AMBROSE-SINGER THEOREM 66
2.5 GENERALIZATION OF MANIFOLDS AND DERIVATIVES 71
2.5.1 MANIFOLD: FRECHET DERIVATIVE AND BANACH MANIFOLD 71
2.5.2 FRECHET MANIFOLD 76
3 THE GROUP OF GENERALIZED LOOPS AND ITS LIE ALGEBRA 80
3.1 INTRODUCTION 80
3.2 THE SHUFFLE ALGEBRA OVER O = /\ M AS A HOPF ALGEBRA 80
3.3 THE GROUP OF LOOPS 87
3.4 THE GROUP OF GENERALIZED LOOPS 87
3.5 GENERALIZED LOOPS AND THE AMBROSE-SINGER THEOREM 92
3.6 THE LIE ALGEBRA OF THE GROUP OF THE GENERALIZED LOOPS 94
4 SHAPE VARIATIONS IN THE LOOP SPACE 100
4.1 PATH DERIVATIVES 100
4.2 AREA DERIVATIVE 107
4.3 VARIATIONAL CALCULUS 117
4.4 FRECHET DERIVATIVE IN A GENERALIZED LOOP SPACE 120
HTTP://D-NB.INFO/1049600223
X CONTENTS
5 WILSON LINES IN HIGH-ENERGY QCD 127
5.1 EIKONAL APPROXIMATION 127
5.1.1 WILSON LINE ON A LINEAR PATH 127
5.1.2 WILSON LINE AS AN EIKONAL LINE 136
5.2 DEEP INELASTIC SCATTERING 139
5.2.1 KINEMATICS 139
5.2.2 INVITATION: THE FREE PARTON MODEL 141
5.2.3 A MORE FORMAL APPROACH 143
5.2.4 PARTON DISTRIBUTION FUNCTIONS 150
5.2.5 OPERATOR DEFINITION FOR PDFS 152
5.2.6 GAUGE INVARIANT OPERATOR DEFINITION 155
5.2.7 COLLINEAR FACTORIZATION AND EVOLUTION OF PDFS 159
5.3 SEMI-INCLUSIVE DEEP INELASTIC SCATTERING 165
5.3.1 CONVENTIONS AND KINEMATICS 166
5.3.2 STRUCTURE FUNCTIONS 167
5.3.3 TRANSVERSE MOMENTUM DEPENDENT PDFS 170
5.3.4 GAUGE-INVARIANT DEFINITION FOR TMDS 172
A MATHEMATICAL VOCABULARY 176
A.L GENERAL TOPOLOGY 176
A.2 TOPOLOGY AND BASIS 177
A.3 CONTINUITY 181
A.4 CONNECTEDNESS 183
A.5 LOCAL CONNECTEDNESS AND LOCAL PATH-CONNECTEDNESS 186
A.6 COMPACTNESS 186
A.7 COUNTABILITY AXIOMS AND BAIRE THEOREM 190
A.8 CONVERGENCE 192
A.9 SEPARATION PROPERTIES 194
A.10 LOCAL COMPACTNESS AND COMPACTIFICATION 195
A.LL QUOTIENT TOPOLOGY 196
A.12 FUNDAMENTAL GROUP 199
A.13 MANIFOLDS 202
A.14 DIFFERENTIAL CALCULUS 205
A.L 5 STOKES'THEOREM 210
A.16 ALGEBRA: RINGS AND MODULES 211
A.17 ALGEBRA: IDEALS 213
A.18 ALGEBRAS 214
A.19 HOPF ALGEBRA 217
A.20 TOPOLOGICAL, C*-, AND BANACH ALGEBRAS 224
A.21 NUCLEAR MULTIPLICATIVE CONVEX HAUSDORFF ALGEBRAS AND THE GEL'FAND
SPECTRUM 225
CONTENTS
* XI
B NOTATIONS AND CONVENTIONS IN QUANTUM FIELD THEORY 232
B.L VECTORS AND TENSORS 232
B.2 SPINORS AND GAMMA MATRICES 233
B.3 LIGHT-CONE COORDINATES 235
B.4 FOURIER TRANSFORMS AND DISTRIBUTIONS 237
B.5 FEYNMAN RULES FOR QCD 238
C COLOR ALGEBRA 240
C.L BASICS 240
C.L.L REPRESENTATIONS 240
C.L.2 PROPERTIES 240
C.2 ADVANCED TOPICS 242
C.2.1 CALCULATING PRODUCTS OF FUNDAMENTAL GENERATORS 242
C.2.2 CALCULATING TRACES IN THE ADJOINT REPRESENTATION 245
D BRIEF LITERATURE GUIDE 248
BIBLIOGRAPHY 249
INDEX 252 |
| any_adam_object | 1 |
| author | Cherednikov, Igor O. Mertens, Tom Veken, Frederik F. van der |
| author_GND | (DE-588)1060734737 (DE-588)1060734818 (DE-588)1060734982 |
| author_facet | Cherednikov, Igor O. Mertens, Tom Veken, Frederik F. van der |
| author_role | aut aut aut |
| author_sort | Cherednikov, Igor O. |
| author_variant | i o c io ioc t m tm f f v d v ffvd ffvdv |
| building | Verbundindex |
| bvnumber | BV042109165 |
| classification_rvk | UO 4060 |
| ctrlnum | (OCoLC)876384241 (DE-599)DNB1049600223 |
| dewey-full | 530.143 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
| dewey-sort | 3530.143 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| indexdate | 2024-08-03T01:50:53Z |
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| isbn | 3110309106 9783110309102 |
| language | English |
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| physical | XI, 257 S. graph. Darst. 240 mm x 170 mm |
| publishDate | 2014 |
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| publisher | De Gruyter |
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| spelling | Cherednikov, Igor O. Verfasser (DE-588)1060734737 aut Wilson lines in quantum field theory Igor O. Cherednikov ; Tom Mertens ; Frederik F. Van der Veken Berlin [u.a.] De Gruyter 2014 XI, 257 S. graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 24 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 DE-604 Mertens, Tom Verfasser (DE-588)1060734818 aut Veken, Frederik F. van der Verfasser (DE-588)1060734982 aut Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038293-8 Erscheint auch als Online-Ausgabe, PDF 978-3-11-030921-8 De Gruyter studies in mathematical physics 24 (DE-604)BV040141722 24 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4625990&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027549633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cherednikov, Igor O. Mertens, Tom Veken, Frederik F. van der Wilson lines in quantum field theory De Gruyter studies in mathematical 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 Igor O. Cherednikov ; Tom Mertens ; Frederik F. Van der Veken |
| title_fullStr | Wilson lines in quantum field theory Igor O. Cherednikov ; Tom Mertens ; Frederik F. Van der Veken |
| title_full_unstemmed | Wilson lines in quantum field theory Igor O. 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 | Quantenfeldtheorie (DE-588)4047984-5 gnd Eichtheorie (DE-588)4122125-4 gnd |
| topic_facet | Quantenfeldtheorie Eichtheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4625990&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027549633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040141722 |
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