Evaluating Feynman integrals

PdftkEmptyString......Page 0
Introduction......Page 10
Notation......Page 17
References......Page 18
Feynman Rules and Feynman Integrals......Page 19
Divergences......Page 22
Alpha Representation......Page 26
Regularization......Page 28
Properties of Dimensionally RegularizedFeynman Integrals......Page 32
References......Page 37
Simple One- and Two-Loop Formulae......Page 39
Recursively One-Loop Feynman Integrals......Page 42
Partial Fractions......Page 43
Dealing with Numerators......Page 44
One-Loop Examples......Page 46
Feynman Parameters......Page 49
Two-Loop Examples......Page 51
References......Page 60
Evaluating by MB Representation......Page 62
One-Loop Examples......Page 63
Multiple MB Integrals......Page 70
More One-Loop Examples......Page 72
Two-Loop Massless Examples......Page 78
Two-Loop Massive Examples......Page 88
Three-Loop Examples......Page 99
More Loops......Page 105
MB Representation versus Expansion by Regions......Page 109
Conclusion......Page 112
References......Page 113
One-Loop Examples......Page 115
Two-Loop Examples......Page 120
Reduction of On-Shell Massless Double Boxes......Page 126
Conclusion......Page 133
References......Page 136
Basic Parametric Representation......Page 139
Constructing Coefficient Functions.  Simple Examples......Page 144
General Recipes. Complicated Examples......Page 152
Two-Loop Feynman Integralsfor the Heavy Quark Potential......Page 158
Conclusion......Page 168
References......Page 169
One-Loop Examples......Page 170
Two-Loop Example......Page 175
Conclusion......Page 178
References......Page 181
Table of Integrals......Page 183
Some Useful Formulae......Page 189
Some Special Functions......Page 191
References......Page 193
Summation Formulae......Page 195
Some Number Series......Page 196
Power Series of Levels 3 and 4in Terms of Polylogarithms......Page 201
Inverse Binomial Power Series up to Level 4......Page 202
Power Series of Levels 5 and 6 in Terms of HPL......Page 204
References......Page 208
MB Integrals with Four Gamma Functions......Page 210
MB Integrals with Six Gamma Functions......Page 217
Analysis of Convergence......Page 223
Practical Sector Decompositions......Page 231
References......Page 234
Dispersion Integrals......Page 235
Gegenbauer Polynomial x-Space Technique......Page 236
Gluing......Page 237
Star-Triangle Relations......Page 238
IR Rearrangement and R*......Page 239
Difference Equations......Page 242
Experimental Mathematics and PSLQ......Page 243
References......Page 245