Feynman Path Integral Formulation

342 Indexthermodynamic analogy, 158, 165Thirring interaction, 90three-dimensional gravity, 21, 182three-graviton vertex, 14three-metric, 104, 136three-sphere, 146tiling of minimal surface, 188, 248time coordinate, 107, 115, 120time evolution, 103, 107torsion, 175total mass of the visible universe, 321transfer matrix, 130transverse traceless modes, 4, 110, 147, 225triangle inequalities, 138, 140, 171, 191trivial infrared fixed points, 82triviality in supersymmetric theories, 39triviality of scalar field theory, 125, 269, 294truncated renormalization group, 96truncation of degrees of freedom, 125tunneling amplitude, 152, 154, 156two-dimensional gravity, 21, 24, 181, 234two-loop divergences for gravity, 91two-phase structure, 82, 92, 264, 284, 294two-point function, 74, 278Uehling radiative corrrection, 98ulraviolet cancellations, 39ultra-local terms, 61ultralocal term, 18, 62, 69ultraviolet behavior, 16ultraviolet cutoff, 16, 31, 48, 52, 56, 63, 68,70, 71, 74, 150, 189, 192, 195, 220, 264,274, 278, 281, 287, 295, 296, 306ultraviolet fixed point, 30, 98, 220, 295, 305ultraviolet regularization, 150uniformly accelerated observer, 163unitarity in higher derivative gravity, 28universal exponent ν, 94, 95, 269, 274, 284,290, 294universal scaling properties, 268, 274, 284,290, 294, 295unphysical degrees of freedom, 127unphysical phase, 285Unruh effect, 163vacumm polarization in QED, 98vacuum contribution, 302vacuum energy density, 10, 311vacuum instability, 47vacuum polarization, 30vacuum state, 133, 156, 159, 163vacuum to vacuum amplitude, 142van Dam - Veltman discontinuity, 9vierbein, 105, 106, 171, 214, 217Virasoro algebra, 40virtual graviton cloud, 308, 314virtual particle pair, 154visible universe, 10volume dependence, 291volume of a face, 172volume of a simplex, 171Voronoi loop, 173Voronoi polyhedra, 199Voronoi volume, 205Ward identities, 2, 185, 232wave function of the universe, 141wave functional, 114, 117, 141, 148weak coupling phase, 288, 300weak field expansion, 1, 225Weyl conformal tensor, 24, 202Weyl spinors, 33Weyl symmetry, 48Wheeler-DeWitt equation, 114, 135, 141Wick rotation, 13, 58, 118, 163, 165Wiener paths, 58Wilson line, 281Wilson loop, 100, 188, 248, 301WKB method, 115, 144, 146, 152, 156, 158world lines, 281world sheet coordinates, 40world-sheet supersymmetry, 48Yang-Mills theories, 71, 84, 98, 127, 248zero energy Schrödinger equation, 114, 141zero lattice spacing limit, 295zero modes, 11, 227, 228, 234, 237, 264zeta function regularization, 19, 148zig-zag motion of a quantum particle, 58, 66