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Bibliographic Details
Main Author:	Smirnov, Vladimir A. 1951- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2006
Subjects:	Calculus, Integral Feynman integrals Quantenfeldtheorie Störungstheorie Pfadintegral
Links:	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
Item Description:	Literaturverz. S. 277 - 283
Physical Description:	IX, 283 S. graph. Darst.
ISBN:	9783540306108 3540306102

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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
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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_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
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