Feynman Path Integral Formulation

Contents1 Continuum Formulation ........................................ 11.1 General Aspects ............................................ 11.2 MasslessSpinTwoField .................................... 11.3 WaveEquation............................................. 21.4 FeynmanRules ............................................ 111.5 One-Loop Divergences . . . . . ................................. 161.6 Gravity in d Dimensions..................................... 211.7 Higher Derivative Terms . . . . ................................. 241.8 Supersymmetry ............................................ 331.9 Supergravity . . . ............................................ 371.10 String Theory . . ............................................ 401.11 Supersymmetric Strings . . . . ................................. 482 Feynman Path Integral Formulation ............................. 552.1 ThePathIntegral........................................... 552.2 SumoverPaths ............................................ 562.3 Eulidean Rotation . . ........................................ 582.4 Gravitational Functional Measure ............................. 592.5 Conformal Instability . . . . . . ................................. 643 Gravity in 2+ε Dimensions ..................................... 673.1 Dimensional Expansion . . . . ................................. 673.2 Perturbatively Non-renormalizable Theories: The Sigma Model .... 683.3 Non-linear Sigma Model in the Large-N Limit .................. 793.4 Self-coupled Fermion Model ................................. 833.5 The Gravitational Case . . . . . ................................. 843.6 Phases of Gravity in 2+ε Dimensions ......................... 923.7 Running of α(μ) in Gauge Theories . . . . . ...................... 98xv