Feynman Path Integral Formulation

336 IndexCauchy problem, 103, 107central charge, 40change of basis in Fock space, 159choice of coordinates, 172choice of time coordinate, 107, 120chromo-electric field, 128classical field equations, 2, 10, 183, 301classical gravity on a lattice, 183closed Friedman universe, 119closed strings, 50closed surface, 247collapsed lattice, 288color singlets, 134compact Euclidean four-geometries, 143compact Euclidean metrics, 118compact groups, 220compact variables, 133compactification assumption, 51complex periodic time, 165complex time, 58, 118, 163conformal anomaly, 24conformal gauge, 24conformal instability, 64, 227, 264, 273conformal invariance, 48conformal mode, 64, 91connected correlation function, 278conserved energy momentum tensor, 1constant curvature metric, 119, 235, 238, 260constraint equations, 103, 107constraints on metric fluctuation, 55, 86, 191continuum limit, 134, 295conventions, xiicoordinate conditions, 103, 110coordinate independence, 306corrections to purely thermal emission, 162correlation between Wilson lines, 281correlation function, 74, 100, 278correlation length, 74, 134, 280, 295correlation length exponent ν, 76, 81, 91, 94,95, 97, 269, 274, 290correlations between curvatures, 245, 248,258, 274, 278, 285cosmological constant, 9, 10, 29, 63, 84, 106,138, 180, 218, 249, 260, 262, 300, 302,315, 321cosmological constraints, 300cosmological solutions, 314cosmological wavefunction, 141counting of microstates, 158coupling renormalization, 87covariant derivative, 106, 211, 215critical coupling, 80, 82, 83, 90, 94, 264, 267,284, 290, 294critical dimension, 24critical dimension of strings, 47, 50critical exponent ν, 76critical exponents, 77, 78critical point, 92, 264, 267, 284, 294, 295cross polytope, 263curvature, 173, 260curvature correlation, 245, 248, 258, 274, 276,278, 285curvature fluctuation, 267, 276curvature scales, 300, 302curvature squared terms, 24, 198, 218, 234,275, 320cutoff, 16, 31, 48, 52, 56, 61–63, 68, 70, 71,74, 139, 192, 195, 220, 242, 264, 267,274, 278, 281, 287, 295, 296, 306cutoff function, 97d’Alambertian operator, 317De Sitter space, 260decoupling, 220DeDonder gauge, 12, 225deficit angle, 171, 262degenerate configurations, 288delta function, 18, 62, 69density of states, 66derivative expansion, 98derivatives of the free energy, 276determinant of the supermetric, 192DeWitt measure, 59, 192, 196, 242, 249DeWitt supermetric, 59, 114, 135, 192diagrammtic expansion, 11diffeomorphism constraint, 112, 118, 120diffeomorphism invariance, 8, 184, 196, 209,220, 234dihedral angle, 171, 262dihedral volume, 199dilaton gravity, 48, 51dimensional expansion, 67, 84dimensional regularization, 11, 18dimensional transmutation, 71, 300dimensional transmutation in gauge theories,98dimensionful coupling constant, 16Dirac γ-matrices, 34, 37, 176, 211, 214, 217Dirac operator, 30, 153, 211Dirac spin matrices, 34, 37, 215, 217Dirichlet boundary conditions, 148distance in function space, 114dual lattice, 176, 178dual of a simplex, 173, 176dual subdivision, 199dust, 123dynamical triangulations, 219