Feynman Path Integral Formulation

Index1/N expansion, 822 + ε expansion for gravity, 843 + 1 formulation of gravity, 107, 183O(2) symmetric spin system, 70, 78O(N) σ-model, 68, 79, 82SL(2,C) group, 217SO(3,1) group, 217SO(d) group, 175SU(N) gauge theories, 71, 127, 213, 248SU(N) generators, 131U(N)-invariant self-coupled fermion model,83β-function for gauge theories, 98β-function for gravity, 92, 274, 298β-function for the O(N) σ-model, 71, 81ε expansion, 67, 77d-dimensional gravity, 11, 21, 260d-simplex, 170n-bein, 106, 171, 211, 214, 217n-dimensional Riemannian manifold, 21p-forms, 172accelerated expansion, 317Acknowledgements, xiiiaction for a scalar field, 203ADM formulation, 107affine connection, 6, 188, 248, 250anomalous dimension, 77, 274, 294anti-De Sitter space, 260anti-periodic boundary condition, 165anti-screening, 308anti-screening in QCD, 98approximate renormalization group, 96astrophysical observations, 300asymptotic freedom, 30, 71, 98asymptotic safety, 67asymptotic series, 77average curvature, 276, 300, 302average edge length, 235average hinge bivector, 256average lattice spacing, 235, 264average volume, 276average volume of a simplex, 264axial gauge, 129axiomatic field theory, 58background field method, 17background gauge fixing, 86background metric, 17, 29, 86, 145, 227Baker-Hausdorff formula, 129bare cosmological constant, 84, 180, 249, 262,277, 288bare Green’s functions, 75barycentric subdivision, 178, 199Bianchi identities, 7, 85, 103, 109, 186black hole entropy, 158black hole evaporation, 166black hole horizon, 154, 163black hole radiance, 154, 158black hole temperature, 155, 158Bogoliubov transformation, 159bordered determinant, 172Borel transform, 47, 77Bose distribution, 162bosonic string, 24, 40branched polymer, 93, 273Brans-Dicke theory, 321Brownian motion, 58Calabi-Yau compactification, 51Callan-Symanzik equations, 75canonical commutation relations, 114canonical form of the field equations, 104canonically conjugate field, 127, 129335