Gravitation, Gauge Theories and the Early Universe

ISBN-13: 9789027727107 / Angielski / Twarda / 1989 / 545 str.

B. R. Iyer; N. Mukunda; C. V. Vishveshwara

Opis

This book evolved out of some one hundred lectures given by twenty experts at a special instructional conference sponsored by the University Grants Commis sion, India. It is pedagogical in style and self-contained in several interrelated areas of physics which have become extremely important in present-day theoretical research. The articles begin with an introduction to general relativity and cosmology as well as particle physics and quantum field theory. This is followed by reviews of the standard gauge models of high-energy physics, renormalization group and grand unified theories. The concluding parts of the book comprise discussions in current research topics such as problems of the early universe, quantum cosmology and the new directions towards a unification of gravitation with other forces. In addition, special concise treatments of mathematical topics of direct relevance are also included. The content of the book was carefully worked out for the mutual education of students and research workers in general relativity and particle physics. This ambitious programe consequently necessitated the involvement of a number of different authors. However, care has been taken to ensure that the material meshes into a unified, cogent and readable book. We hope that the book will serve to initiate and guide a student in these different areas of investigation starting from first principles and leading to the exciting current research problems of an interdisciplinary nature in the context of the origin and structure of the universe."

Spis treści

I: Gravitation and Cosmology.- 1. Introduction to General Relativity.- 1. From Special Theory to General Theory.- 2. Einstein’s Thought Experiment.- 3. Geometry or Geometries?.- 4. Riemannian Geometry and Geodesics.- 5. Geometry and Gravitation.- 6. The Line Element.- 7. Summation Convention.- 8. Vectors and Tensors.- 9. Quotient Law.- 10. The Fundamental Tensor.- 11. Raising and Lowering the Suffixes (Indices).- 12. Length of a Vector.- 13. Addition of Vectors at a Point.- 14. Covariant Derivative of a Contravariant Vector.- 15. Covariant Derivative of a Covariant Vector.- 16. The Christoffel Symbols.- 17. Geodesics.- 18. The Curvature Tensor.- 19. Natural Coordinates at a Point.- 20. Symmetry Properties of the Curvature Tensor.- 21. Bianchi Identities and the Ricci Tensor.- 22. The Einstein Tensor and the Field Equations of Gravitation.- 23. Matter Tensor for a Perfect Fluid.- 24. Exercises.- 2. Introduction to Black Holes.- 1. Preamble.- 2. The Schwarzschild Black Hole.- 3. Properties of the Schwarzschild Black Hole.- 4. The Kerr Black Hole.- 5. The Black Hole and the Ergosphere.- 6. The Penrose Process.- 7. Charged Black Holes.- 8. Conclusion.- References.- 3. Black-Hole Thermodynamics and Hawking Radiation.- 4. Introduction to Relativistic Cosmology.- 1. Preamble.- 2. The Cosmic Spacetime.- 3. Cosmological Models.- 4. Dust Models.- 5. Radiation Models.- 6. Models with Nonzero Cosmological Constants.- 7. Observational Contacts.- 8. Conclusion.- References.- 5. Relics of the big Bang.- 1. The Early Universe.- 2. Thermodynamics of the Early Universe.- 3. Primordial Neutrinos.- 4. The Neutron/Proton Ratio.- 5. The Synthesis of Helium and Other Nuclei.- 6. The Microwave Background.- 7. Anisotropies of the Microwave Background.- 8. Cosmology and Particle Physics.- 9. Survival of Massive Particles.- 10. Problems of the Very Early Universe.- References.- 6. An Approach to Anisotropic Cosmologies.- 1. Motivation.- 2. Killing Vectors and Bianchi Types.- 3. Kinematics — Analysis of the Velocity Field.- 4. Perfect Fluid Solutions Classified According to Kinematic Properties.- 5. Some Anisotropic Cosmological Solutions.- 6. Problems.- 7. Topics in Spacetime Structure.- 1. Introduction.- 2. The Manifold Model.- 3. Spacetime Diffeomorphisms.- 4. Killing Vector Fields.- 5. Boundary Attachment and Conformal Campactification for Spacetimes.- References.- 8. Differential Forms and Einstein-Cartan Theory.- 1. Basic Definitions.- 2. Algebra and Calculus of Forms.- 3. Connection and Curvature Forms.- 4. Einstein-Cartan Theory — The Gauge Theory of Gravity.- 5. Gravitation in the Presence of Fermionic Matter.- References.- II: Introduction to Particle Physics and Gauge Field Theories.- 9. Introduction to Classical and Quantum Lagrangian Field Theory.- 1. Classical Lagrangian Field Theory.- 2. Canonical Quantization.- 3. Discrete Symmetries.- 4. Interacting Fields.- 5. Invariant Perturbation Theory.- 6. Primitive Divergences in QED.- 7. QED as a Renormalizable Theory.- 8. V-A as a Nonrenormalizable Theory.- 9. Dimensional Regularization.- Further Reading.- 10. Introduction to Particle Physics, Symmetries and Conservation Laws.- 1. Introduction.- 2. Charge Independence of Nuclear Forces — Isotopic Spin.- 3. Strange Particles.- 4. Nucleon Number Conservation.- 5. Lepton Number Conservation.- 6. Discrete Symmetries.- 7. ?5-Invariance and Weak Interactions.- 8. Strong Interactions: Quarks and Gluons.- 9. Need for Colour.- 10. Gauge Invariance.- Further Reading.- 11. Building up the Standard Gauge Model of High-Energy Physics.- 1. Introduction.- 2. U(1) Gauge Theory.- 3. Spontaneous Breakdown of Symmetry — Goldstone Model.- 4. Higgs Model.- 5. SU(2) Gauge Theory.- 6. Spontaneous Breakdown of SU(2) Symmetry.- 7. One More Model.- 8. General Case of Non-Abelian Symmetry Breakdown.- 9. SU(2) x U(1) Model.- 10. ‘Standard Model’ before Gauge Theory.- 11. Current Algebra and SU(2) x U(1) Charges of the Fermions.- 12. The Electroweak Gauge Theory.- 13. Consequences of the Electroweak Theory.- 14. Renormalizability.- 15. Spontaneous Symmetry Breaking and Phase Transitions.- 16. Deep Inelastic Scatterng, Asymptotic Freedom and Colour SU(3).- 17. The Renormalization Group Equation.- 18. Formal Derivation of the Renormalization Group Equation.- 19. Solution of the Renormalization Group Equation.- 20. Hydrodynamic Analogy.- 21. Fixed Points and Asymptotic Freedom.- 22. Asymptotic Freedom of QCD.- 23. Infrared Problem and Colour Confinement.- 24. Tests of QCD.- 25. The Standard Model of High Energy Physics.- 26. Beyond the Standard Model.- References.- 12. Introduction to Grand Unification Theories.- 1. Grand Unification — A Survey of Basic Ideas.- 2. Grand Unified Theory Based on G = SU(5).- 3. Spontaneous Symmetry Breaking.- 4. Predictions of Minimal SU(5).- 5. Baryon Asymmetry.- 6. Phase Transitions in the Early Universe.- 13. Topology and Homotopy.- 1. What is Topology?.- 2. Why the Recent Interest in Topology?.- 3. Homotopy Theory.- 4. Chern Classes.- References.- 14. Introduction to Compact Simple Lie Groups.- III: Quantum Effects in the Early Universe and Approaches to the Unification of Fundamental Forces.- 15. Quantum Field Theory in Curved Spacetime: Canonical Quantization.- 1. Quantum Field Theory in Curved Spacetime.- 2. Canonical Quantization of the Scalar Field in CST.- 3. The Conformal Vacuum.- 4. A Toy Model with Particle Creation.- 5. The Adiabatic Vacuum.- References.- 16. Zeta Function Regularisation and Effective Action in Curved Spacetime.- 1. The Riemann Zeta Function.- 2. Applications.- 3. Path Integral Formulation for QFT in CST.- 4. Conformal Anomalies.- 5. Phase Transition in a De Sitter Universe.- References.- 17. Inflationary Cosmology and Quantum Effects in the Early Universe.- 1. Quantum Field Theory in Curved Spacetime: A Short History.- 2. Problems in Standard Cosmology.- 3. Inflation.- 4. Free Lunch.- 5. The ‘New’ Model.- 6. Evolution of the Scalar Field.- 7. Linde’s Chaotic Inflation.- 8. Hawking’s Limits on Inflationary Models.- 9. Quantum Effects in the Early Universe.- 10. The Fundamental Problem.- 11. De Witt-Schwinger Expansion of Green’s Function.- 12. Renormalization.- 13. Other Methods.- 14. Example of Back Reaction.- 15. Applications.- References.- 18. Quantum Cosmology — The Story So Far.- 1. Introduction.- 2. Minisuperspace of Conformal Degree of Freedom.- 3. Quantized FRW Universes.- 4. Applications of Quantum Gravity.- 5. Critique, Comparison and Open Questions.- Appendix 1: Schrödinger Approach to Field Theory.- Appendix 2: The Wheeler-De Witt Equation.- Notes and References.- 19. The Photon, the Graviton and the Gravitino.- 1. The Photon.- 2. The Graviton.- 3. The Gravitino.- 4. The Rarita-Schwinger Lagrangian.- 20. The Vierbein, Vielbeins and Spinors in Higher Dimensions.- 1. The Vierbein.- 2. Vielbeins.- 3. Spinors in d-dimensions.- 21. Kaluza-Klein Theories.- 1. Kaluza-Klein Theories.- 2. Spontaneous Compactification and Isometry Groups.- 3. Harmonic Expansions, Chiral Fermions and All That.- References.- 22. Kaluza-Klein Cosmology.- 1. Introduction.- 2. Five-Dimensional Kaluza-Klein Theory.- 3. Remarks.- 4. Dimensional Reduction.- 5. Cosmology.- References.- 23. An Elementary Introduction to the Gauge Theory Approach to Gravity.- 1. Introduction.- 2. The Yang-Mills Construction.- 3. Gauging a Special Relativistic Matter Lagrangian.- 4. Kinematics of the Gravitational Variables.- 5. The Gravitational Action.- 6. Translational Gauge Potentials.- References.- 24. Graded Lie Algebras.- 1. Introduction.- 2. Examples of Graded Lie Algebras (GLAs).- 3. Maps of GLAs.- 4. Classification of GLAs.- References.- 25. Supersymmetry and Supergravity.- 1. Introduction.- 2. Coleman-Mandula Theorem and Supersymmetry Algebra.- 3. Representation of the Supersymmetry Algebra on One-Particle States.- 4. Representations of the Supersymmetry Algebra on Fields and Invariant Lagrangians.- 5. Spontaneous Breakdown of Supersymmetry.- 6. Pure N = 1 Supergravity in Four Dimensions.- 7. N = 1, D = 11 Supergravity.- 8. N = 1, D = 10 Supergravity.- 9. Concluding Remarks.- References.- 26. An Overview of Superstring Theory.- 1. Introduction.- 2. Duality.- 3. The Veneziano Formula.- 4. Free Relativistic String.- 5. Orthonormal Gauge.- 6. Quantization.- 7. Light Cone Quantization.- 8. Hamiltonian Formalism.- 9. Quantization.- 10. Lorentz Covariance.- 11. Spectrum.- 12. Closed Strings.- 13. Interacting Strings.- 14. Field Theory Limit.- 15. Superstrings.- 16. Problems and Prospects.- References.