EVALUATING FEYNMAN INTEGRALS
CONTENTS INTRODUCTION NOTATION REFERENCES FEYNMAN INTEGRALS: BASIC DE?NITIONS AND TOOLS FEYNMAN RULES AND FEYNMAN INTEGRALS DIVERGENCES ALPHA REPRESENTATION REGULARIZATION PROPERTIES OF DIMENSIONALLY REGULARIZED FEYNMAN INTEGRALS EVALUATING BY ALPHA AND FEYNMAN PARAMETERS SIMPLE ONE- AND TWO-LOOP FORMULAE AUXILIARY TRICKS RECURSIVELY ONE-LOOP FEYNMAN INTEGRALS PARTIAL FRACTIONS DEALING WITH NUMERATORS ONE-LOOP EXAMPLES FEYNMAN PARAMETERS TWO-LOOP EXAMPLES EVALUATING BY MB REPRESENTATION MULTIPLE MB INTEGRALS MORE ONE-LOOP EXAMPLES TWO-LOOP MASSLESS EXAMPLES TWO-LOOP MASSIVE EXAMPLES THREE-LOOP EXAMPLES MORE LOOPS MB REPRESENTATION VERSUS EXPANSION BY REGIONS CONCLUSION IBP AND REDUCTION TO MASTER INTEGRALS REDUCTION OF ON-SHELL MASSLESS DOUBLE BOXES REDUCTION TO MASTER INTEGRALS BY BAIKOV’S METHOD BASIC PARAMETRIC REPRESENTATION CONSTRUCTING COE?CIENT FUNCTIONS SIMPLE EXAMPLES GENERAL RECIPES COMPLICATED EXAMPLES TWO-LOOP FEYNMAN INTEGRALS FOR THE HEAVY QUARK POTENTIAL EVALUATION BY DI?ERENTIAL EQUATIONS TWO-LOOP EXAMPLE