Principles of quantum general relativity / Edward Prugovecki.

Format:

Book

Author/Creator:

Prugovecki, Eduard.

Language:

English

Subjects (All):

Quantum theory.

General relativity (Physics).

Physical Description:

xxii, 350 p.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c1995.

Language Note:

English

Summary:

This monograph explains and analyzes the principles of a quantum-geometric framework for the unification of general relativity and quantum theory. By taking advantage of recent advances in areas like fibre and superfibre bundle theory, Krein spaces, gauge fields and groups, coherent states, etc., these principles can be consistently incorporated into a framework that can justifiably be said to provide the foundations for a quantum extrapolation of general relativity. This volume aims to present this approach in a way which places as much emphasis on fundamental physical ideas as on their precise mathematical implementation. References are also made to the ideas of Einstein, Bohr, Born, Dirac, Heisenberg and others, in order to set the work presented here in an appropriate historical context.

Contents:

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. Poincaré covariance and relativistic quantum localizability. 3.7. Poincaré 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.

ch. 5. Massive quantum-geometric boson fields. 5.1. Microcausality vs. Local commutativity of quantum fields. 5.2. Quantum frame fields and microcausality. 5.3. Second-quantized boson frames in Fock bundles. 5.4. Propagators for parallel transport in Fock bundles. 5.5. Geometric localization of boson field exciton modes. 5.6. Quantum-geometric boson field propagation in free fall. 5.7. Quantum field interactions and relativistic locality. 5.8. Quantum-geometric propagation of interacting boson fields

ch. 6. Massive quantum-geometric fermion fields. 6.1. Fock-Dirac bundles and bispinor quantum frame fields. 6.2. Standard Berezin-Dirac quantum superfibres. 6.3. Quantum Berezin-Dirac superfibre bundles. 6.4. Parallel transport in Fock-Dirac bundles. 6.5. Geometrically localized fermion field supermodes. 6.6. Quantum-geometric fermion field propagation

ch. 7. Massless quantum-geometric gauge fields. 7.1. Hilbert space representations of the Poincaré group. 7.2. Krein space representations of the Poincaré group. 7.3. Typical Krein fibres for spin-1 bosons. 7.4. Gupta-Bleuler bundles for multi-photon states. 7.5. Quantum-geometric propagation in Gupta-Bleuler bundles. 7.6. The geometric interpretation of Yang-Mills gauge fields. 7.7. Global gauge transformations on principal bundles. 7.8. BRST and anti-BRST operators on spaces of connections. 7.9. The Quantum-Geometric Framework for Yang-Mills Fields

ch. 8. Quantum-geometric gravity. 8.1. Diffeomorphism and Poincaré gauge invariance in CGR. 8.2. Basic aspects of quantum-geometric gravity. 8.3. Superlocal graviton states and internal gauges. 8.4. Linearly and circularly polarized graviton states. 8.5. Quantum gravitational and Berezin-Faddeev-Popov frames. 8.6. Quantum gravitational gauge supergroups and quantum spacetime. 8.7. Quantum gravitational connections and BRST symmetries. 8.8. Superlocal quantum gravitational and matter fields. 8.9. Quantum-geometric evolution of gravitational and matter fields. 8.10. Summary and conclusion.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references(p.[323]-340)and index.

ISBN:

9789812831385

981283138X