Gravity, gauge theories, and quantum cosmology

by Jayant V. Narlikar and T. Padmanabhan

[目次]

  • 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 Schrodinger 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.

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この本の情報

書名 Gravity, gauge theories, and quantum cosmology
著作者等 Narlikar, Jayant Vishnu
Padmanabhan, T.
Padmanabhan T.
シリーズ名 Fundamental theories of physics
出版元 Reidel
刊行年月 c1986
ページ数 xv, 468 p.
大きさ 24 cm
ISBN 9027719489
NCID BA00175813
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言語 英語
出版国 オランダ
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