Feynman Path Integral Formulation

Index 339
lattice supermetric, 135
lattice weak field expansion, 225
lattice Wheeler-DeWitt equation, 135
lattice zero modes, 227, 228, 234, 237, 264
least action principle, 56
Legendre transform, 96
Lehman representation, 134
length of a curve, 195
Lense-Thirring effect, 321
LEP experiment, 98
Lie derivative, 8
light-cone gauge, 40
linear potential, 134
linearized gravity, 1, 27, 110, 147, 225
Liouville field, 24, 47, 90
Lipschitz-Killing curvatures, 198
local averages, 276
local curvature, 173
local gauge invariance, 2, 8, 98, 184, 196, 209,
220, 234, 240
local rotations, 8
local scale transformation, 8
local shears, 8
logarithmic divergence, 314
long distance regime, 280
long range correlations, 220
loop bivector, 256
loop quantization, vii, 107
Lorentz frames, 105, 173
Lorentz group, 33, 106, 217
Mach’s principle, 321
magnetic field, 133
Majorana spinors, 33, 48
mass gap, 74, 82, 84, 134
mass renormalization, 35
massless spin two field, 1
matter fields, 90, 112, 119, 123, 203
mean field theory, 254, 260
measure parameter, 62
method of steepest descent, 144
metric, 1
metric fluctuation, 55, 86, 191
metric perturbation, 145
metric signature, xii, 11
mini black holes, 166
minimal surface, 176, 188, 248
minisuperspace, 118
minisuperspace models, 122
modified field equations, 302, 305, 314
modified Newtonian potential, 15, 302, 314
modified static isotropic solution, 311
momentum constraint, 112, 118
momentum cutoff, 31, 62, 74, 220, 306
N=8 supergravity, 39
naive expectation for the running of G, 93
Nambu-Goto string, 40
negative curvature, 260
Newton’s constant, 1, 10, 84
Newtonian limit, 22, 121
Nielsen-Hughes formula, 39
non-abelian gauge theories, 98
non-analytic contributions, 77
non-analyticity in the partition function, 245,
284, 295
non-compact groups, 220
non-linear σ-model, 68, 79, 298
non-linear nature of gravity, 6
non-local effective action, 306
non-perturbative scale Λ MS ,98
non-perturbative vacuum contribution, 302
non-relativistic matter, 123
non-relativistic path integral, 56, 142
non-renormalizable theories, 16, 67
non-rotating black hole, 154
non-trivial ultraviolet fixed point, 67, 76, 84,
93, 295
numerical simulations, 273
observables, 276
octahedral tessellation, 236
on-shell counterterm, 19
one-dimensional Coulomb problem, 66
one-dimensional gravity, 195, 209
one-loop beta function, 39
one-loop divergences, 16, 31
one-loop divergences for gravity, 19, 39, 91
one-loop effective action, 31
one-loop renormalization group β-function,
73, 89, 98
open strings, 50
operator ordering ambiguity, 40, 114, 120, 123
order parameter, 77
origin of inertia, 321
oscillatory wavefunction, 123
Padé approximants, 244
Painlevé coordinates, 156
pair creation, 152, 154
Palatini formulation, 104, 180
Palatini identity, 105
parallel transport, 173, 188, 248
particle orbits, 314
particle thermal emission, 155, 158, 162
partition function, 135
path ordered exponential, 100
Pauli paramagnetism, 39
Pauli-Fierz mass term, 9