Holdings: Analytic tools for Feynman integrals

Analytic tools for Feynman integrals:

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Bibliographic Details
Main Author:	Smirnov, Vladimir A. 1951- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer [2012]
Series:	Springer Tracts in Modern Physics 250
Subjects:	Pfadintegral
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	ix, 296 Seiten Illustrationen
ISBN:	3642348858 9783642348853 9783642439254

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MARC


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adam_text	IMAGE 1 CONTENTS 1 INTRODUCTION 1 1.1 NOTATION 10 REFERENCES 10 2 FEYNMAN INTEGRALS: BASIC DEFINITIONS AND TOOLS 11 2.1 FEYNMAN RULES AND FEYNMAN INTEGRALS 11 2.2 DIVERGENCES 14 2.3 ALPHA REPRESENTATION 19 2.4 REGULARIZATION 21 2.5 PROPERTIES O F DIMENSIONALLY REGULARIZED FEYNMAN INTEGRALS 26 REFERENCES 30 3 EVALUATING BY ALPHA AND FEYNMAN PARAMETERS 33 3.1 SIMPLE ONE- AND TWO-LOOP FORMULAE 33 3.2 AUXILIARY TRICKS 37 3.2.1 RECURSIVELY ONE-LOOP FEYNMAN INTEGRALS 37 3.2.2 PARTIAL FRACTIONS 38 3.2.3 DEALING WITH NUMERATORS 38 3.3 ONE-LOOP EXAMPLES 41 3.4 FEYNMAN PARAMETERS 4 5 3.5 TWO-LOOP EXAMPLES 48 REFERENCE . . 58 4 SECTOR DECOMPOSITIONS 61 4.1 HEPP AND SPEER SECTORS 62 4.2 RECURSIVE SECTOR DECOMPOSITIONS 68 4.3 GEOMETRICAL SECTOR DECOMPOSITIONS 72 4.4 ANALYSIS O F CONVERGENCE AND A DEFINITION O F DIMENSIONALLY REGULARIZED UV AND IR DIVERGENT FEYNMAN INTEGRALS 75 REFERENCES 80 VII HTTP://D-NB.INFO/1027026672 IMAGE 2 VIII C O N T E N T S 5 EVALUATING BY MB REPRESENTATION 83 5.1 A ONE-LOOP EXAMPLE 84 5.2 EVALUATING MULTIPLE MB INTEGRALS 89 5.3 HOW TO DERIVE AND CHECK MB REPRESENTATIONS 9 0 5.4 TWO BASIC STRATEGIES O F RESOLVING SINGULARITIES IN E 100 5.5 TWO-LOOP EXAMPLES 102 5.6 EXAMPLES WITH THE OLD STRATEGY A 106 5.7 APPLYING MB REPRESENTATION TO EXPAND FEYNMAN INTEGRALS IN MOMENTA AND MASSES 119 5.8 COMBINING MB REPRESENTATION WITH SECTOR DECOMPOSITIONS TO EXPAND FEYNMAN INTEGRALS 121 5.9 CONCLUSION 123 REFERENCES 124 6 IBP AND REDUCTION TO MASTER INTEGRALS 127 6.1 SOLVING IBP RELATIONS BY HAND 128 6.2 GENERAL SETUP FOR IBP REDUCTION 134 6.3 LAPORTA'S ALGORITHM 136 6.4 ALGEBRAIC STRUCTURE OF IBP RELATIONS 138 6.5 BAIKOV'S METHOD 140 6.6 SHIFTING DIMENSION AND GROBNER BASES 148 6.7 OBTAINING ADDITIONAL RELATIONS 151 6.8 CONCLUSION 153 REFERENCES 154 7 EVALUATION BY DIFFERENTIAL EQUATIONS 157 7.1 ONE-LOOP EXAMPLES 157 7.2 TWO-LOOP EXAMPLE 163 7.3 THREE-LOOP EXAMPLE 167 7.4 CONCLUSION 169 REFERENCES 171 8 EVALUATING MASTER INTEGRALS BY DIMENSIONAL RECURRENCE AND ANALYTICITY 173 8.1 DIMENSIONAL RECURRENCE RELATIONS 173 8.2 GENERAL PRESCRIPTIONS 175 8.3 MULTILOOP EXAMPLES 179 8.4 EVALUATING MULTICOMPONENT MASTER INTEGRALS 193 8.5 WHAT NUMBERS CAN APPEAR IN EPSILON EXPANSIONS? 200 REFERENCES 202 9 ASYMPTOTIC EXPANSIONS IN MOMENTA AND MASSES 203 9.1 EXPANSION BY SUBGRAPHS 203 9.2 EXPANSION BY REGIONS 208 IMAGE 3 CONTENTS I X 9.3 EXPANSION BY REGIONS IN PARAMETRIC REPRESENTATIONS 214 9.4 HOW TO REVEAL RELEVANT REGIONS 216 9.5 REVEALING POTENTIAL REGIONS 219 9.6 REVEALING GLAUBER REGIONS 221 9.7 MATHEMATICAL STATUS O F EXPANSION BY REGIONS 225 REFERENCES 226 10 APPENDIX A: TABLES 227 10.1 TABLE OF INTEGRALS 227 10.2 SOME USEFUL FORMULAE 234 11 APPENDIX B: SOME SPECIAL FUNCTIONS 237 REFERENCES 241 12 APPENDIX C: SUMMATION FORMULAE 243 12.1 SOME NUMBER SERIES 244 12.2 POWER SERIES OF WEIGHTS 3 AND 4 IN TERMS OF POLYLOGARITHMS 249 12.3 INVERSE BINOMIAL POWER SERIES UP TO WEIGHT 4 250 12.4 POWER SERIES O F WEIGHTS 5 AND 6 IN TERMS OF HPLS 252 REFERENCES 257 13 APPENDIX D: TABLE OF M B INTEGRALS 259 13.1 MB INTEGRALS WITH FOUR GAMMA FUNCTIONS 259 13.2 MB INTEGRALS WITH SIX GAMMA FUNCTIONS 267 13.3 THE GAUSS HYPERGEOMETRIC FUNCTION AND MB INTEGRALS 272 14 APPENDIX E: A BRIEF REVIEW O F SOME OTHER METHODS 275 14.1 DISPERSION INTEGRALS 275 14.2 GEGENBAUER POLYNOMIAL X-SPACE TECHNIQUE 277 14.3 GLUING 278 14.4 STAR-TRIANGLE RELATIONS 279 14.5 DUALITY FOR PLANAR GRAPHS 280 14.6 IR REARRANGEMENT AND R * 282 14.7 DIFFERENCE EQUATIONS 284 14.8 EXPERIMENTAL MATHEMATICS AND PSLQ 285 14.9 EVALUATING FEYNMAN INTEGRALS BY SUMMING UP SERIES 287 14.10 SYMBOLS 287 REFERENCES 290 LIST O F SYMBOLS 293 INDEX 295
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author	Smirnov, Vladimir A. 1951-
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author_facet	Smirnov, Vladimir A. 1951-
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spelling	Smirnov, Vladimir A. 1951- Verfasser (DE-588)10336627X aut Analytic tools for Feynman integrals Vladimir A. Smirnov Berlin ; Heidelberg Springer [2012] ix, 296 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer Tracts in Modern Physics 250 Pfadintegral (DE-588)4173973-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-34886-0 Springer Tracts in Modern Physics 250 (DE-604)BV000000153 250 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4164529&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=025702976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Smirnov, Vladimir A. 1951- Analytic tools for Feynman integrals Springer Tracts in Modern Physics Pfadintegral (DE-588)4173973-5 gnd
subject_GND	(DE-588)4173973-5
title	Analytic tools for Feynman integrals
title_auth	Analytic tools for Feynman integrals
title_exact_search	Analytic tools for Feynman integrals
title_full	Analytic tools for Feynman integrals Vladimir A. Smirnov
title_fullStr	Analytic tools for Feynman integrals Vladimir A. Smirnov
title_full_unstemmed	Analytic tools for Feynman integrals Vladimir A. Smirnov
title_short	Analytic tools for Feynman integrals
title_sort	analytic tools for feynman integrals
topic	Pfadintegral (DE-588)4173973-5 gnd
topic_facet	Pfadintegral
url	http://deposit.dnb.de/cgi-bin/dokserv?id=4164529&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=025702976&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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