Principles Of Quantum General Relativity
by Eduard PrugoveДЌki /
1995 / English / PDF
109.7 MB Download
Ch. 1. Survey of principal historical developments. 1.1. From special to general relativity. 1.2. Geometry as part of physical theory. 1.3. Quantum theory and the idea of fundamental length. 1.4. Localizability and renormalizability in quantum field theory. 1.5. Quantum field theory in curved spacetime. 1.6. From canonical quantum gravity to superstrings ch. 2. Classical frame bundles in general relativity. 2.1. General covariance under coordinate transformations. 2.2. General covariance and classical frame bundles. 2.3. Moving frames in principal frame bundles. 2.4. Gauge invariance in associated bundles. 2.5. Connections and gauge transformations. 2.6. Levi-Civita connections and the strong equivalence principle. 2.7. The Einstein field equations and canonical gravity ch. 3. Quantum frames and spacetime localizability. 3.1. The uncertainty principle and representations of the Galilei group. 3.2. Quantum mechanics and informational completeness. 3.3. Informationally complete nonrelativistic quantum frames. 3.4. Sharp-point limits of nonrelativistic quantum frames. 3.5. Path integration and nonrelativistic quantum frames. 3.6. Poincar covariance and relativistic quantum localizability. 3.7. Poincar covariance and quantum Lorentz frames. 3.8. Fundamental special-relativistic quantum Lorentz frames ch. 4. Quantum geometry over a classical base spacetime. 4.1. Quantum frame bundles and associated bundles. 4.2. The internal Hilbert structure of quantum bundles. 4.3. Connections on affine frame bundles and associated bundles. 4.4. Connections and parallel transport in quantum bundles. 4.5. Quantum tensorial bundles and quantum metrics. 4.6. Quantum-geometric propagation in quantum bundles. 4.7. The physical meaning of quantum-geometric propagation. 4.8. Relativistic causality of classical and quantum propagation
