Gravity, Gauge Theories and Quantum Cosmology

ISBN-13: 9789401085083 / Angielski / Miękka / 2011 / 468 str.

Jayant Vishnu Narlikar;T. Padmanabhan

Opis

For several decades since its inception, Einstein's general theory of relativity stood somewhat aloof from the rest of physics. Paradoxically, the attributes which normally boost a physical theory - namely, its perfection as a theoreti cal framework and the extraordinary intellectual achievement underlying i- prevented the general theory from being assimilated in the mainstream of physics. It was as if theoreticians hesitated to tamper with something that is manifestly so beautiful. Happily, two developments in the 1970s have narrowed the gap. In 1974 Stephen Hawking arrived at the remarkable result that black holes radiate after all. And in the second half of the decade, particle physicists discovered that the only scenario for applying their grand unified theories was offered by the very early phase in the history of the Big Bang universe. In both cases, it was necessary to discuss the ideas of quantum field theory in the background of curved spacetime that is basic to general relativity. This is, however, only half the total story. If gravity is to be brought into the general fold of theoretical physics we have to know how to quantize it. To date this has proved a formidable task although most physicists would agree that, as in the case of grand unified theories, quantum gravity will have applications to cosmology, in the very early stages of the Big Bang universe. In fact, the present picture of the Big Bang universe necessarily forces us to think of quantum cosmology."

Spis treści

1 / Introduction.- 1.1. Historical Background.- 1.2. What This Book is About.- I Quantum Theory.- 2 / Path Integrals.- 2.1. Action in Classical Physics.- 2.2. Action in Quantum Physics.- 2.3. The Path Integral.- 2.4. The Quadratic Action.- 2.5. The Schrödinger Equation.- 2.6. The Spreading of Wave Packets.- 2.7. The Harmonic Oscillator.- Notes and References.- 3 / En Route to Quantum Field Theory.- 3.1. The Field as a Dynamical System.- 3.2. Harmonic Oscillator in an External Potential.- 3.3. The Vacuum Persistence Amplitude.- 3.4. Euclidean Time.- 3.5. The Double-Hump Potential.- 3.6. The Instanton Solutions.- 3.7. The Concept of an Effective Action.- 3.8. Quantum Mechanics at Finite Temperature.- Notes and References.- 4 / Quantum Field Theory.- 4.1. Classical Field Theory (General).- 4.2. Classical Field Theory (Specific Fields).- 4.3. Quantization of the Scalar Field.- 4.4. Canonical Quantization.- 4.5. Scalar Field with Quartic Self-interaction.- 4.6. Nonperturbative Methods.- 4.7. Quantum Theory in External Fields.- 4.8. Field Theory at Finite Temperature.- Notes and References.- 5 / Gauge Fields.- 5.1. Gauge Invariance — Electromagnetism.- 5.2. Gauge Invariance — Generalized.- 5.3. General Formalism for Gauge Theory.- 5.4. Spontaneous Symmetry Breaking.- 5.5. SSB with an Abelian Gauge Field.- 5.6. SSB with a Nonabelian Gauge Field.- 5.7. The Salam—Weinberg Model.- 5.8. The Coleman—Weinberg Mechanism.- 5.9. The Gauge Field as a Physical System.- 5.10. The Gauge Field Vacuum and Instantons.- 5.11. Solitons — Monopole Solution.- Notes and References.- II Classical General Relativity.- 6 / General Theory of Relativity.- 6.1. The Need for a General Theory of Relativity.- 6.2. Curved Spacetime.- 6.3. Vectors and Tensors.- 6.4. Metric and Geodesics.- 6.5. Parallel Transport.- 6.6. The Curvature Tensor.- 6.7. Physics in Curved Spacetime.- 6.8. Einstein’s Field Equations.- 6.9. The Newtonian Approximation.- 6.10. The ? Term.- 6.11 Conformal Transformations.- Notes and References.- 7 / Gravitating Massive Objects.- 7.1. The Schwarzschild Solution.- 7.2. Experimental Tests of General Relativity.- 7.3. Gravitational Radiation.- 7.4. Geometrodynamics.- 7.5. Gravitational Collapse.- 7.6. Black Holes.- Notes and References.- 8 / Relativistic Cosmology.- 8.1. Cosmological Symmetries.- 8.2. The Friedmann Models.- 8.3. Observational Cosmology.- 8.4. The Early Universe.- 8.5. The Problems of Singularity, Horizon, and Flatness.- 8.6. Anisotropic Cosmologies.- Notes and References.- III Quantization in Curved Spacetime.- 9 / Quantum Theory in Curved Spacetime.- 9.1. Quantum Theory in a Curved Background: Why?.- 9.2. General Covariance and the Particle Concept.- 9.3. Field Theory in Robertson-Walker Spacetime.- 9.4. Field Theory in de Sitter Spacetime.- 9.5. Euclideanization and the Thermal Green’s Functions.- 9.6. Field Theory in the Black-Hole Spacetime.- Notes and References.- 10 / The Very Early Universe.- 10.1. Symmetry Breaking in the Early Universe.- 10.2. Cosmological Monopoles.- 10.3. Cosmological Inflationary Scenarios.- 10.4. The Guth Inflation.- 10.5. Inflation with the Coleman—Weinberg Potential.- 10.6. Fine-Tunings in the Early Universe.- Notes and References.- IV Quantum Cosmology.- 11 / Approaches to Quantum Cosmology.- 11.1. Introduction.- 11.2. The Linearized Theory.- 11.3. Canonical Quantization.- 11.4. Manifestly Covariant Quantization.- 11.5. Path Integrals in Euclidean Spacetime.- 11.6. Concluding Remarks.- Notes and References.- 12 / Quantum Conformal Fluctuations.- 12.1. Quantum Gravity via Path Integrals.- 12.2. Conformal Fluctuations.- 12.3. QCF of Friedmann Cosmologies.- 12.4. Bianchi Type I Cosmologies.- 12.5. Universes with Arbitrary Distributions of Massive Particles.- 12.6. The Problems of Singularity and Horizons.- 12.7. The Problem of Flatness.- 12.8. Further Developments.- Notes and References.- 13 / Towards a More Complete Theory.- 13.1. Towards a More Complete Theory.- 13.2. The Average Metric.- 13.3. Quantum Fluctuations and Proper Length.- 13.4. Lower Bound to Proper Length.- 13.5. Quantum Stationary Geometries.- 13.6. QSG and the Back Reaction on the Metric.- 13.7. Solutions of Quantum Gravity Equations.- 13.8. Cosmogenesis and Vacuum Instability.- Notes and References.- 14 / Epilogue.- V Appendices.- Appendix A/Renormalization.- Appendix B/Basic Group Theory.- B.1. Definition of a Group.- B.2. Generators.- B.3. Representations.- Appendix C/Differential Geometry.- C.1. Basic Concepts.- C.2. Vectors and 1-Forms.- C.3. Lie Derivative and Covariant Derivative.- C.4. Curvature and Metric.- Appendix D/Spacetime Symmetries.- D.1. Displacement of Spacetime.- D.2. Killing Vectors.- D.3. Homogeneity.- D.4. Isotropy.