Feynman integral calculus:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 277 - 283 |
| Physical Description: | IX, 283 S. graph. Darst. |
| ISBN: | 9783540306108 3540306102 |
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| 245 | 1 | 0 | |a Feynman integral calculus |c Vladimir A. Smirnov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
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Record in the Search Index
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| adam_text | VLADIMIR A. SMIRNOV FEYNMAN INTEGRAL CALCULUS &J SPRINGER CONTENTS 1
INTRODUCTION 1 1.1 NOTATION 9 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 OF
DIMENSIONALLY REGULARIZED FEYNMAN INTEGRALS 25 3 EVALUATING BY ALPHA AND
FEYNMAN PARAMETERS 31 3.1 SIMPLE ONE- AND TWO-LOOP FORMULAE 31 3.2
AUXILIARY TRICKS 34 3.2.1 RECURSIVELY ONE-LOOP FEYNMAN INTEGRALS 34
3.2.2 PARTIAL FRACTIONS 35 3.2.3 DEALING WITH NUMERATORS 36 3.3 ONE-LOOP
EXAMPLES 38 3.4 FEYNMAN PARAMETERS 43 3.5 TWO-LOOP EXAMPLES 45 PROBLEMS
54 4 EVALUATING BY MB REPRESENTATION 57 4.1 ONE-LOOP EXAMPLES 58 4.2
EVALUATING MULTIPLE MB INTEGRALS 65 4.3 MORE ONE-LOOP EXAMPLES 68 4.4
TWO-LOOP MASSLESS EXAMPLES 74 4.5 TWO-LOOP MASSIVE EXAMPLES 84 4.6
THREE-LOOP EXAMPLES 95 4.7 MORE LOOPS 102 4.8 MB REPRESENTATION VERSUS
EXPANSION BY REGIONS 105 4.9 CONCLUSION 109 PROBLEMS 112 VIII CONTENTS 5
IBP AND REDUCTION TO MASTER INTEGRALS 115 5.1 ONE-LOOP EXAMPLES 116 5.2
TWO-LOOP EXAMPLES 121 5.3 REDUCTION OF ON-SHELL MASSLESS DOUBLE BOXES
128 5.4 CONCLUSION 135 PROBLEMS 138 6 REDUCTION TO MASTER INTEGRALS BY
BAIKOV S METHOD 139 6.1 BASIC PARAMETRIC REPRESENTATION 139 6.2
CONSTRUCTING COEFFICIENT FUNCTIONS. SIMPLE EXAMPLES 144 6.3 GENERAL
RECIPES. COMPLICATED EXAMPLES 153 6.4 TWO-LOOP FEYNMAN INTEGRALS FOR THE
HEAVY QUARK STATIC POTENTIAL 159 6.5 CONCLUSION 169 PROBLEMS 171 7
EVALUATION BY DIFFERENTIAL EQUATIONS 173 7.1 ONE-LOOP EXAMPLES 173 7.2
TWO-LOOP EXAMPLE 178 7.3 CONCLUSION 182 PROBLEMS 184 A TABLES 185 A.I
TABLE OF INTEGRALS 185 A.2 SOME USEFUL FORMULAE 191 B SOME SPECIAL
FUNCTIONS 195 C SUMMATION FORMULAE 199 C.I SOME NUMBER SERIES 200 C.2
POWER SERIES OF LEVELS 3 AND 4 IN TERMS OF POLYLOGARITHMS 205 C.3
INVERSE BINOMIAL POWER SERIES UP TO LEVEL 4 206 C.4 POWER SERIES OF
LEVELS 5 AND 6 IN TERMS OF HPL 208 D TABLE OF MB INTEGRALS 213 D.I MB
INTEGRALS WITH FOUR GAMMA FUNCTIONS 213 D.2 MB INTEGRALS WITH SIX GAMMA
FUNCTIONS 220 D.3 THE GAUSS HYPERGEOMETRIC FUNCTION AND MB INTEGRALS 225
CONTENTS IX E ANALYSIS OF CONVERGENCE AND SECTOR DECOMPOSITIONS 227 E.I
ANALYSIS OF CONVERGENCE 227 E.2 PRACTICAL SECTOR DECOMPOSITIONS 235 F A
BRIEF REVIEW OF SOME OTHER METHODS 239 F.I DISPERSION INTEGRALS 239 F.2
GEGENBAUER POLYNOMIAL A SPACE TECHNIQUE 240 F.3 GLUING 241 F.4
STAR-TRIANGLE RELATIONS 242 F.5 IR REARRANGEMENT AND R* 243 F.6
DIFFERENCE EQUATIONS 246 F.7 EXPERIMENTAL MATHEMATICS AND PSLQ 247 G
APPLYING GROBNER BASES TO SOLVE IBP RELATIONS 251 G.I GROBNER BASES FOR
IDEALS OF POLYNOMIALS 251 G.2 CONSTRUCTING GROBNER-TYPE BASES FOR IBP
RELATIONS 255 G.3 EXAMPLES 258 G.4 PERSPECTIVES 261 SOLUTIONS 263
REFERENCES 277 LIST OF SYMBOLS 285 INDEX 287
|
| adam_txt |
VLADIMIR A. SMIRNOV FEYNMAN INTEGRAL CALCULUS &J SPRINGER CONTENTS 1
INTRODUCTION 1 1.1 NOTATION 9 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 OF
DIMENSIONALLY REGULARIZED FEYNMAN INTEGRALS 25 3 EVALUATING BY ALPHA AND
FEYNMAN PARAMETERS 31 3.1 SIMPLE ONE- AND TWO-LOOP FORMULAE 31 3.2
AUXILIARY TRICKS 34 3.2.1 RECURSIVELY ONE-LOOP FEYNMAN INTEGRALS 34
3.2.2 PARTIAL FRACTIONS 35 3.2.3 DEALING WITH NUMERATORS 36 3.3 ONE-LOOP
EXAMPLES 38 3.4 FEYNMAN PARAMETERS 43 3.5 TWO-LOOP EXAMPLES 45 PROBLEMS
54 4 EVALUATING BY MB REPRESENTATION 57 4.1 ONE-LOOP EXAMPLES 58 4.2
EVALUATING MULTIPLE MB INTEGRALS 65 4.3 MORE ONE-LOOP EXAMPLES 68 4.4
TWO-LOOP MASSLESS EXAMPLES 74 4.5 TWO-LOOP MASSIVE EXAMPLES 84 4.6
THREE-LOOP EXAMPLES 95 4.7 MORE LOOPS 102 4.8 MB REPRESENTATION VERSUS
EXPANSION BY REGIONS 105 4.9 CONCLUSION 109 PROBLEMS 112 VIII CONTENTS 5
IBP AND REDUCTION TO MASTER INTEGRALS 115 5.1 ONE-LOOP EXAMPLES 116 5.2
TWO-LOOP EXAMPLES 121 5.3 REDUCTION OF ON-SHELL MASSLESS DOUBLE BOXES
128 5.4 CONCLUSION 135 PROBLEMS 138 6 REDUCTION TO MASTER INTEGRALS BY
BAIKOV'S METHOD 139 6.1 BASIC PARAMETRIC REPRESENTATION 139 6.2
CONSTRUCTING COEFFICIENT FUNCTIONS. SIMPLE EXAMPLES 144 6.3 GENERAL
RECIPES. COMPLICATED EXAMPLES 153 6.4 TWO-LOOP FEYNMAN INTEGRALS FOR THE
HEAVY QUARK STATIC POTENTIAL 159 6.5 CONCLUSION 169 PROBLEMS 171 7
EVALUATION BY DIFFERENTIAL EQUATIONS 173 7.1 ONE-LOOP EXAMPLES 173 7.2
TWO-LOOP EXAMPLE 178 7.3 CONCLUSION 182 PROBLEMS 184 A TABLES 185 A.I
TABLE OF INTEGRALS 185 A.2 SOME USEFUL FORMULAE 191 B SOME SPECIAL
FUNCTIONS 195 C SUMMATION FORMULAE 199 C.I SOME NUMBER SERIES 200 C.2
POWER SERIES OF LEVELS 3 AND 4 IN TERMS OF POLYLOGARITHMS 205 C.3
INVERSE BINOMIAL POWER SERIES UP TO LEVEL 4 206 C.4 POWER SERIES OF
LEVELS 5 AND 6 IN TERMS OF HPL 208 D TABLE OF MB INTEGRALS 213 D.I MB
INTEGRALS WITH FOUR GAMMA FUNCTIONS 213 D.2 MB INTEGRALS WITH SIX GAMMA
FUNCTIONS 220 D.3 THE GAUSS HYPERGEOMETRIC FUNCTION AND MB INTEGRALS 225
CONTENTS IX E ANALYSIS OF CONVERGENCE AND SECTOR DECOMPOSITIONS 227 E.I
ANALYSIS OF CONVERGENCE 227 E.2 PRACTICAL SECTOR DECOMPOSITIONS 235 F A
BRIEF REVIEW OF SOME OTHER METHODS 239 F.I DISPERSION INTEGRALS 239 F.2
GEGENBAUER POLYNOMIAL A SPACE TECHNIQUE 240 F.3 GLUING 241 F.4
STAR-TRIANGLE RELATIONS 242 F.5 IR REARRANGEMENT AND R* 243 F.6
DIFFERENCE EQUATIONS 246 F.7 EXPERIMENTAL MATHEMATICS AND PSLQ 247 G
APPLYING GROBNER BASES TO SOLVE IBP RELATIONS 251 G.I GROBNER BASES FOR
IDEALS OF POLYNOMIALS 251 G.2 CONSTRUCTING GROBNER-TYPE BASES FOR IBP
RELATIONS 255 G.3 EXAMPLES 258 G.4 PERSPECTIVES 261 SOLUTIONS 263
REFERENCES 277 LIST OF SYMBOLS 285 INDEX 287 |
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| language | English |
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| spelling | Smirnov, Vladimir A. 1951- Verfasser (DE-588)10336627X aut Feynman integral calculus Vladimir A. Smirnov Berlin [u.a.] Springer 2006 IX, 283 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 277 - 283 Calculus, Integral Feynman integrals Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Störungstheorie (DE-588)4128420-3 s Pfadintegral (DE-588)4173973-5 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015501439&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smirnov, Vladimir A. 1951- Feynman integral calculus Calculus, Integral Feynman integrals Quantenfeldtheorie (DE-588)4047984-5 gnd Störungstheorie (DE-588)4128420-3 gnd Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4128420-3 (DE-588)4173973-5 |
| title | Feynman integral calculus |
| title_auth | Feynman integral calculus |
| title_exact_search | Feynman integral calculus |
| title_exact_search_txtP | Feynman integral calculus |
| title_full | Feynman integral calculus Vladimir A. Smirnov |
| title_fullStr | Feynman integral calculus Vladimir A. Smirnov |
| title_full_unstemmed | Feynman integral calculus Vladimir A. Smirnov |
| title_short | Feynman integral calculus |
| title_sort | feynman integral calculus |
| topic | Calculus, Integral Feynman integrals Quantenfeldtheorie (DE-588)4047984-5 gnd Störungstheorie (DE-588)4128420-3 gnd Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Calculus, Integral Feynman integrals Quantenfeldtheorie Störungstheorie Pfadintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015501439&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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