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Quantum Field Theory and Topology [1993]
- 1
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Introduction
- 6
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Definitions and Notations
- 13
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The Simplest Lagrangians
- 17
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Quadratic Lagrangians
- 19
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Internal Symmetries
- 24
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Gauge Fields
- 28
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Particles Corresponding to Nonquadratic Lagrangians
- 30
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Lagrangians of Strong, Weak and Electromagnetic Interactions
- 37
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Grand Unifications
- 43
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Topologically Stable Defects
- 56
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Topological Integrals of Motion
- 62
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A Two-Dimensional Model. Abrikosov Vortices
- 68
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’t Hooft—Polyakov Monopoles
- 74
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Topological Integrals of Motion in Gauge Theory
- 80
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Particles in Gauge Theories
- 83
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The Magnetic Charge
- 89
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Electromagnetic Field Strength and Magnetic Charge in Gauge Theories
- 94
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Extrema of Symmetric Functionals
- 97
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Symmetric Gauge Fields
- 104
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Estimates of the Energy of a Magnetic Monopole
- 109
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Topologically Non-Trivial Strings
- 115
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Particles in the Presence of Strings
- 122
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Nonlinear Fields
- 128
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Multivalued Action Integrals
- 132
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Functional Integrals
- 138
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Applications of Functional Integrals to Quantum Theory
- 146
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Quantization of Gauge Theories
- 158
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Elliptic Operators
- 163
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The Index and Other Properties of Elliptic Operators
- 169
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Determinants of Elliptic Operators
- 173
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Quantum Anomalies
- 183
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Instantons
- 194
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The Number of Instanton Parameters
- 199
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Computation of the Instanton Contribution
- 207
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Functional Integrals for a Theory Containing Fermion Fields
- 216
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Instantons in Quantum Chromodynamics
- 223
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Topological Spaces
- 225
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Groups
- 229
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Gluings
- 233
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Equivalence Relations and Quotient Spaces
- 235
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Group Representations
- 241
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Group Actions
- 245
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The Adjoint Representation of a Lie Group
- 247
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Elements of Homotopy Theory
- 257
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Applications of Topology to Physics