Feynman Path Integral Formulation
Feynman Path Integral Formulation
Feynman Path Integral Formulation
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Index<br />
1/N expansion, 82<br />
2 + ε expansion for gravity, 84<br />
3 + 1 formulation of gravity, 107, 183<br />
O(2) symmetric spin system, 70, 78<br />
O(N) σ-model, 68, 79, 82<br />
SL(2,C) group, 217<br />
SO(3,1) group, 217<br />
SO(d) group, 175<br />
SU(N) gauge theories, 71, 127, 213, 248<br />
SU(N) generators, 131<br />
U(N)-invariant self-coupled fermion model,<br />
83<br />
β-function for gauge theories, 98<br />
β-function for gravity, 92, 274, 298<br />
β-function for the O(N) σ-model, 71, 81<br />
ε expansion, 67, 77<br />
d-dimensional gravity, 11, 21, 260<br />
d-simplex, 170<br />
n-bein, 106, 171, 211, 214, 217<br />
n-dimensional Riemannian manifold, 21<br />
p-forms, 172<br />
accelerated expansion, 317<br />
Acknowledgements, xiii<br />
action for a scalar field, 203<br />
ADM formulation, 107<br />
affine connection, 6, 188, 248, 250<br />
anomalous dimension, 77, 274, 294<br />
anti-De Sitter space, 260<br />
anti-periodic boundary condition, 165<br />
anti-screening, 308<br />
anti-screening in QCD, 98<br />
approximate renormalization group, 96<br />
astrophysical observations, 300<br />
asymptotic freedom, 30, 71, 98<br />
asymptotic safety, 67<br />
asymptotic series, 77<br />
average curvature, 276, 300, 302<br />
average edge length, 235<br />
average hinge bivector, 256<br />
average lattice spacing, 235, 264<br />
average volume, 276<br />
average volume of a simplex, 264<br />
axial gauge, 129<br />
axiomatic field theory, 58<br />
background field method, 17<br />
background gauge fixing, 86<br />
background metric, 17, 29, 86, 145, 227<br />
Baker-Hausdorff formula, 129<br />
bare cosmological constant, 84, 180, 249, 262,<br />
277, 288<br />
bare Green’s functions, 75<br />
barycentric subdivision, 178, 199<br />
Bianchi identities, 7, 85, 103, 109, 186<br />
black hole entropy, 158<br />
black hole evaporation, 166<br />
black hole horizon, 154, 163<br />
black hole radiance, 154, 158<br />
black hole temperature, 155, 158<br />
Bogoliubov transformation, 159<br />
bordered determinant, 172<br />
Borel transform, 47, 77<br />
Bose distribution, 162<br />
bosonic string, 24, 40<br />
branched polymer, 93, 273<br />
Brans-Dicke theory, 321<br />
Brownian motion, 58<br />
Calabi-Yau compactification, 51<br />
Callan-Symanzik equations, 75<br />
canonical commutation relations, 114<br />
canonical form of the field equations, 104<br />
canonically conjugate field, 127, 129<br />
335
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