Gravitation, gauge theories and differential geometry

Physics Reports

Volumn 66, Issue 6, 1980, Pages 213-393

  Eguchi, Tohru ^a,b   Gilkey, Peter B ^c,d   Hanson, Andrew J ^e,f  

^a SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

^c PRINCETON UNIVERSITY   (United States)

^d UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^e UNIVERSITY OF CALIFORNIA   (United States)

^f NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968282200     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/0370-1573(80)90130-1     Document Type: Review

References (172)

1. Axial-Vector Vertex in Spinor Electrodynamics
2. Index Theorem for Manifolds with Boundary
3. Clifford Modules
4. Index of Elliptic Operators I
5. Index of Elliptic Operators II
6. Index of Elliptic Operators III
7. Index of Elliptic Operators IV
8. Index of Elliptic Operators V
9. On the Heat Equation and the Index Theorem
10. Spectral Asymmetry and Riemannian Geometry
11. Spectral Asymmetry and Riemannian Geometry I
12. Spectral Asymmetry and Riemannian Geometry II
13. Spectral Asymmetry and Riemannian Geometry III
14. Deformations of Instantons
15. Self-Duality in Four Dimensional Riemannian Geometry
16. Instantons and Algebraic Geometry
17. Construction of Instantons
18. The Geometrical Interpretation of the Faddeev-Popov Determinant
19. New Gravitational Instantons and Universal Spin Structures
20. The Renormalizable Theory of Gravitation and the Einstein Equations
21. Pseudoparticle Solutions of the Yang-Mills Equations
22. Asymptotically Euclidean Bianchi IX Metrics in Quantum Gravity
23. ()→ γγ in the σ model
24. Sur les varietes d'Einstein compactes
25. Instanton Parameters for Arbitrary Gauge Groups
26. Some Remarks on the Paper of Callias
27. Stability and Gap Phenomena for Yang-Mills Fields
28. Die Auflosung der Rationalen Singularitaten Holomorphen Abbildungen
29. Propagations Functions in Pseudoparticle Fields
30. Massless Excitations in Pseudoparticle Fields
31. Metriques Kahleriennes et Fibres Holomorphes
32. Axial Anomalies and Index Theorems on Open Spaces
33. The Structure of the Gauge Theory Vacuum
34. A Mechanism for Quark Confinement
35. On the Curvature Integral in a Riemannian Manifold
36. Characteristic Forms and Geometric Invariants
37. General Self-Dual Yang-Mills Solutions
38. Axial and Conformal Anomalies for Arbitrary Spin in Gravity and Supergravity
39. New Gravitational Index Theorems and Super Theorems
40. Scalar Field Theory and Exact Solutions to a Classical SU(2) Gauge Theory
41. A Green Function for the General Self-Dual Gauge Field
42. The axial and Trace Anomalies for Spin 3/2
43. A New Classical Solution of the Yang-Mills Fields Equations
44. Quantum Theory of Gravity: I. The Canonical Theory
45. Quantum Theory of Gravity: II. The Manifestly Covariant Theory
46. Quantum Theory of Gravity: III. Applications of the Covariant Theory
47. Quantized Singularities in the Electromagnetic Field
48. η-Invariants and Boundaries of Hermitian Manifolds
49. The Gravitational Corrections to PCAC
50. Gauge Theory in Terms of Projector-Valued Fields
51. Quantum Gravity and World Topology
52. Topological Invariants and Absence of an Axial Anomaly for a Euclidean Taub-NUT (Newman-Unti-Tamburino) Metric
53. Asymptotically Flat Self-Dual Solutions to Euclidean Gravity
54. Self-Dual Solutions to Euclidean Gravity
55. Feynman Diagrams for the Yang-Mills Field
56. The Surface Term in Gauge Theories
57. Action Integrals and Partition Functions in Quantum Gravity
58. Gravitational Multi-Instantons
59. Classification of Gravitational Instanton Symmetries
60. Path Integrals and the Indefiniteness of the Gravitational Action
61. Quantizing Gravitational Instantons
62. 2 as a Gravitational Instanton
63. The Positive Action Conjecture and Asymptotically Euclidean Metrics in Quantum Gravity
64. Index Theorem Boundary Terms for Gravitational Instantons
65. The Boundary Integrand in the Formula for the Signature and Euler Characteristic of a Riemannian Manifold with Boundary
66. Multiple Meron Solutions of the Classical Yang-Mills Equations
67. Instability of Non-Abelian Gauge Theories and Impossibility of Choice of Coulomb Gauge
68. Quantization of Non-Abelian Gauge Theories
69. Zero Energy Solutions of the Dirac Equation in an N-Pseudoparticle Field
70. Gravitational Instanton Contribution to Spin 3/2 Axial Anomaly
71. Stable Vector Bundles and Instantons
72. Gravitational Instantons
73. Spacetime Foam
74. The Propagation of Particles in Spacetime Foam
75. Generalized Spin Structures in Quantum Gravity
76. Symmetry Breaking by Instantons in Supergravity
77. Harmonic Spinors
78. Compact Four-Dimensional Einstein Manifolds
79. Polygons and Gravitons
80. Quantum Meaning of Classical Field Theory
81. Conformal Properties of Pseudoparticle Configurations
82. Conformal Properties of a Yang-Mills Pseudoparticles
83. Vacuum Periodicity in a Yang-Mills Quantum Theory
84. Degree of Freedom in Pseudoparticle Systems
85. An Existence Theorem for Multimeron Solutions to Classical Yang-Mills Field Equations
86. Spineurs Harmoniques
87. Geometric Definition of Gauge Invariance
88. Introduction to the Fiber-Bundle Approach to Gauge Theories
89. Existence of Universal Connections I
90. Existence of Universal Connections II
91. Approaches to the Gravitational Spin-3/2 Axial Anomaly
92. Classical Anomalies and Local Version of the Atiyah-Singer Theorem
93. Anomalous Currents in Curved Space
94. Taub-NUT Instanton with a Horizon
95. A Compact Rotating Gravitational Instanton
96. A Physical Picture of the K3 Gravitational Instanton
97. Anomalies in Supergravity
98. Equivalence of Eguchi-Hanson Metric to Two Center Gibbons-Hawking Metric
99. Axial Vector Anomalies and the Index Theorem in Charged Schwarzschild and Taub-NUT Spaces
100. R-torsion and the Laplacian on Riemannian Manifolds
101. Analytic Torsion for Complex Manifolds
102. Elementary Particles: Classical Mechanics to the Rescue?
103. Axial Anomaly and Boundary Terms for Spinor Fields
104. Fractional Winding Numbers and Surface Effects
105. Incompressible Minimal Surfaces, Three-Dimensional Manifolds with Non-Negative Scalar Curvature and the Positive Mass Conjecture in General Relativity
106. Proof of the Positive Action Conjecture in General Relativity
107. On the Proof of the Positive Mass Conjecture in General Relativity
108. Positivity of the Total Mass of a General Space-Time
109. On Regular Solutions of Euclidean Yang-Mills Equations
110. On Quantum Fluctuations of Instantons
111. Instantons and Fermions in the Field of Instanton
112. The Partition Function of a Degenerate Functional
113. Some Remarks on the Gribov Ambiguity
114. Symmetry Breaking through Bell-Jackiw Anomalies
115. Computation of the Quantum Effects due to a Four Dimensional Pseudoparticle
116. Fiber Bundles associated with Space-Time
117. Solutions of Maxwell and Yang-Mills Equations Associated with Hopf Fiberings
118. Removable Singularities in Yang-Mills Fields
119. Invariant Theoretical Interpretation of Interaction
120. On Self-Dual Gauge Fields
121. Some Exact Multipseudoparticle Solutions of Classical Yang-Mills Theory
122. Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields
123. Conservation of Isotopic Spin and Isotopic Gauge Invariance
124. On Calabi's Conjecture and Some New Results on Algebraic Geometry
125. On the Ricci Curvature of a Compact Kähler Manifold and the Complex Monge-Ampere Equation
126. Role of Conformal Three-Geometry in the Dynamics of Gravitation
127. Gauge Theories
128. Geometry of Characteristic Classes
129. The Use of Instantons
130. The Geometrical Setting of Gauge Theories of the Yang-Mills Type
131. Fiber Bundle Techniques in Gauge Theories
132. Classical and Semiclassical Solutions to Yang-Mills Theory
133. An Introduction to the Atiyah-Singer Index Theorem
134. Introductory Lectures on Fiber Bundles and Topology for Physicists