Knots and Feynman diagrams:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge lecture notes in physics
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 258 S. Ill., graph. Darst. |
| ISBN: | 0521587611 |
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Datensatz im Suchindex
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IMAGE 1
KNOTS AND FEYNMAN DIAGRAMS
DIRK KREIMER MAINZ UNIVERSITY
* CAMBRIDGE
**** UNIVERSITY PRESS
IMAGE 2
CONTENTS
ACKNOWLEDGEMENTS PAGE XI
1 INTRODUCTION 1
1.1 MOTIVATION 1
2 PERTURBATIVE QUANTUM FIELD THEORY 7
2.1 PQFT 7
2.1.1 CANONICAL QUANTIZATION 7
2.1.2 PERTURBATION THEORY 10
2.1.3 FEYNMAN RULES 15
2.1-4 SCHWINGER-DYSON EQUATIONS 17
2.2 REGULARIZATION 21
2.2.1 DIMENSIONAL REGULARIZATION 23
2.3 BASIC FACTS ABOUT RENORMALIZATION 25
2.3.1 MULTIPLICATIVE RENORMALIZATION 26
2.3.2 POWER COUNTING 29
3 THE HOPF ALGEBRA STRUCTURE OF RENORMALIZATION 36
3.1 PRELIMINARIES 36
3.2 VERTEX CORRECTIONS 41
3.2.1 THE FIRST ITERATION 41
3.2.2 THE FACTORIZATION 44
3.3 OVERLAPPING DIVERGENCES 48
3.3.1 A TOY MODEL 49
3.4 TECHNICALITIES 52
3-4-1 FORM FACTORS 53
3.4.2 OTHER DEGREES OF DIVERGENCE 54
3.5 TOWARDS A HOPF ALGEBRA 56
3.6 FEYNMAN DIAGRAMS AS A REALIZATION 61
3.7 THE HOPF ALGEBRA 67
3.1.1 THE COPRODUCT 72
3.7.2 THE ANTIPODE 75
VII
IMAGE 3
VIII CONTENTS
3.8 REALIZATIONS OF * 80
3.8.1 TOY MODELS 80
3.8.2 QUANTUM FIELD THEORIES 87
3.8.3 ONCE MORE: OVERLAPPING DIVERGENCES 90
3.9 AN ULTIMATE EXAMPLE 93
3.10 REMARKS 94
4 RATIONALITY: NO KNOTS, NO TRANSCENDENTALS 97
4.1 A COMBINATORIAL APPROACH 99
4.2 DELBOURGO'S ARGUMENT 102
4.3 TOY MODELS VERSUS QFT 103
5 THE SIMPLEST LINK DIAGRAMS 106
5.1 LINK DIAGRAMS FROM LADDER DIAGRAMS 106
5.1.1 DISENTANGLING THE LINK DIAGRAM 108
5.1.2 GAUSS CODES 112
5.2 LINKS AND LADDERS - THE OVERLAPPING CASE 114
6 NECESSARY TOPICS FROM KNOT THEORY 118
6.1 BASICS 118
6.2 TORUS KNOTS 121
6.3 BRAIDS 123
6.4 KNOT POLYNOMIALS 125
7 KNOTS TO NUMBERS: (2,2N - 3) TORUS KNOTS AND
C ( 2 N - 3) 130
7.1 (3) FROM A COUNTERTERM 130
7.2 THE (2,Q) TORUS KNOTS AND ((Q) 134
7.3 FACTOR KNOTS 139
7.4 GAUSS CODES 141
8 ONE-LOOP WORDS 143
8.1 DEFINITIONS 144
8.2 AN ELEMENTARY EXAMPLE 147
8.3 CONTINUATION TO A DRESSED TWO-LOOP GRAPH 154
8.4 HIGHER ORDER DRESSING 160
9 EULER-ZAGIER SUMS 163
9.1 RELATIONS COMING FROM THE DRINFELD ASSOCIATOR 165
9.2 SHUFFLE ALGEBRAS 168
9.3 EULER-ZAGIER SUMS AND MZVS 169
IMAGE 4
CONTENTS
IX
10 KNOTS AND TRANSCENDENTALS 174
10.1 THE (3,4) TORUS KNOT AND THE FIRST EULER DOUBLE SUM 176 W.L.LTHE
KNOT 819 AND ITS KNOT-NUMBER 177
10.1.2A MOMENTUM ROUTING ANALYSIS 179
10.1.** GAUSS CODE ANALYSIS 182
LO.L.^CHORD DIAGRAMS, KNOTS AND NUMBERS TO FIVE LOOPS 183 10.2 $ 4
-THEORY: MORE KNOTS AND NUMBERS 183
10.3 RATIONALITY AND THE /3-FUNCTION OF QUENCHED QED 189
10.4 EULER DOUBLE SUMS 193
10.5 FIELD THEORY, KNOT THEORY, NUMBER THEORY 196
10.6 FROM KNOTS TO NUMBERS 199
10.6.1 HOW MANY KNOT NUMBERS? 200
10.6.2KNOT-NUMBERS FROM EVALUATIONS OF FEYNMAN DIAGRAMS 201
10.6.3POSITIVE KNOTS ASSOCIATED WITH IRREDUCIBLE MZVS 205
11 THE FOUR-TERM RELATION 214
11.1 INTRODUCTION 214
11.2 THE 4TR BETWEEN PRIMITIVE GRAPHS 218
11.3 A TEST 232
11.4 HOPF ALGEBRA AND 4TR 234
12 HOPF ALGEBRAS, NON-COMMUTATIVE GEOMETRY, AND WHAT ELSE? 236
12.1 THE HOPF ALGEBRA HR OF ROOTED TREES 236
12.1.1 FORMULAE FOR RENORMALIZATION 241
12.2 THE RELATION BETWEEN UR AND ** 243
12.3 AND WHAT ELSE? 247
REFERENCES INDEX
253 259 |
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| isbn | 0521587611 |
| language | English |
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| series2 | Cambridge lecture notes in physics |
| spelling | Kreimer, Dirk Verfasser aut Knots and Feynman diagrams Dirk Kreimer 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2000 XII, 258 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge lecture notes in physics 13 Feynman diagrams Knot theory Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Feynman-Graph (DE-588)4154291-5 gnd rswk-swf Hopf-Algebra (DE-588)4160646-2 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Feynman-Graph (DE-588)4154291-5 s Knotentheorie (DE-588)4164318-5 s Hopf-Algebra (DE-588)4160646-2 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Cambridge lecture notes in physics 13 (DE-604)BV009623742 13 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008879623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kreimer, Dirk Knots and Feynman diagrams Cambridge lecture notes in physics Feynman diagrams Knot theory Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Feynman-Graph (DE-588)4154291-5 gnd Hopf-Algebra (DE-588)4160646-2 gnd Knotentheorie (DE-588)4164318-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4154291-5 (DE-588)4160646-2 (DE-588)4164318-5 |
| title | Knots and Feynman diagrams |
| title_auth | Knots and Feynman diagrams |
| title_exact_search | Knots and Feynman diagrams |
| title_full | Knots and Feynman diagrams Dirk Kreimer |
| title_fullStr | Knots and Feynman diagrams Dirk Kreimer |
| title_full_unstemmed | Knots and Feynman diagrams Dirk Kreimer |
| title_short | Knots and Feynman diagrams |
| title_sort | knots and feynman diagrams |
| topic | Feynman diagrams Knot theory Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd Feynman-Graph (DE-588)4154291-5 gnd Hopf-Algebra (DE-588)4160646-2 gnd Knotentheorie (DE-588)4164318-5 gnd |
| topic_facet | Feynman diagrams Knot theory Quantum field theory Quantenfeldtheorie Feynman-Graph Hopf-Algebra Knotentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008879623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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