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| Marathe K.B., Martucci G. — The mathematical foundations of gauge theories |
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| Предметный указатель |
Group, real symplectic 35
Group, reducible 47
Group, special linear 27
Group, special orthogonal 27
Group, special unitary 28 34
Group, unitary 28 34
Group, unitary symplectic 37
Haax measure 27
Hamiltonian 25
Hamilton’s equations 26
Hausdorff space 299
Higgs bundle 248
Higgs bundle, generalized 250
Higgs field 188 248
Higgs field, generalized 188 250
Higgs mass 258
Higgs mechanism 254
Higgs phenomenon 254
Higgsons 261
Hilbert — Einstein action 197
Hirzebruch polynomial 121
Hirzebruch signature 187
Hirzebruch signature, operator 187
Hirzebruch signature, theorem 187
Hodge decomposition theorem 98
Hodge star operator 20
Hodge-deRham operator 22
Holonomy bundle 56
Holonomy group 55-56
Holonomy group, restricted 55-56
Homeomorphism 298
Homogeneous element 315
Homogeneous element, degree of 315
Homogeneous ideal 315
Homogeneous space 28
Homologous 310
Homology 89 310
Homology class, singular 90
Homology module 310
Homology module, relative singular 92
Homology module, singular 90
Homology sequence 93
Homology sequence, long exact 312
Homology, differentiable singular 96
Homology, singular 89
Homotopic maps 75
Homotopic maps, relatively 75
Homotopically equivalent 77
Homotopy 75
Homotopy group,  -th 81
Homotopy group, first 76
Homotopy group, stable 87
Homotopy type 77
Hopf fibering 63 85
Hopf fibration 63
Hopf invariant 105
Hopf space 83
Horizontal curve 55
Horizontal lift of 54 64 71
Horizontal lift of, a curve 55
Horizontal lift of, a vector field 54
Horizontal space 71
Horizontal subspace 54
Ideal 309
Ideal, principal 309
Immersion 11
INDEX 176 178
Index bundle 278
Index, analytic 178
Index, topological 178
Infinitely smoothing 174
Inner multiplication 17
Instanton 216 225
Instanton, center of 228
Instanton, complex 237
Instanton, deformation complex 237
Instanton, equation 215 225
Instanton, gravitational 197
Instanton, number 215 225 229
Instanton, size of 228
integral 18
Integral curve 15
Integral domain 309
Interior 4
Intermediate value property 301
Intersection form 99
Intersection form, equivalent 100
Intersection form, even 101
Intersection form, odd 101
Intersection form, of type I 101
Intersection form, of type II 101
Invariant symmetric polynomial 116
Isomorphism 304
Isotropic 318
Isotropy group 28
Isotropy subgroup 262
jet 42
Jet, extension 42
Jet, extension map 42
Jet, of sections 42
Jones polynomial 284
K nneth formula 97
Killing form 45
Kirby — Siebenmann invariant 103
Knot 79
Knot, equivalent 79
Knot, group 79
Knot, invariant 80
Laplace — Beltrami operator 22
Laplacian operator 22
Laplacian operator, classical 22
Laplacian operator, on forms 22
Left-handed fermions 258
Levi — Civita connection 69
Lie algebra 9
Lie algebra, homomorphism 10
Lie algebra, of a Lie group 30
Lie bracket 9
Lie derivative 15
Lie group 26
Lie group, action of 28
Lie group, anti-homomorphism 26
Lie group, automorphism 26
Lie group, homomorphism 26
Lie group, isomorphism 26
Lie subgroup 27
Local base 299
Local coordinate chart 2
Local coordinate representation 40
Local flow 15
Local orientation 93
Local trivialization 40
Locally compact 300
Locally connected 301
Locally finite 300
Locally finite family 300
Loop 75
Loop space, -th 83
Loop space, first 82
Lorentz connection 69
Magnetic induction 205
Magnetic tension 205
Manifold 2
Manifold, complex 2
Manifold, differentiable 2
Manifold, differential 2
Manifold, dimension of 2
Manifold, Lorentz 19
Manifold, orientable 14 94
Manifold, oriented 14 94
| Manifold, pseudo — Riemannian 19
Manifold, real 2
Manifold, Riemannian 19
Manifold, symplectic 24
Manifold, topological 2
Manifold, with boundary 4
Mathai — Quillen formalism 276
Maxwell action 201
Maxwell connection 201
Maxwell field 201
Maxwell potential 201
Metric 298
Metric connection 69
Metric space 298
Metric volume form 20
Metric,  Riemannian 153
Metric, Hermitian 43
Metric, non-degenerate 19
Metric, Riemannian 43
Metric, strong Riemannian 157
Metric, weak Riemannian 153
Metrizable 298
Minimal coupling 191 251
Minimal interaction 191
Mixed double complex 313
Mixing angle 257
Moduli space of instantons 235
monopole 265
Monopole, configuration space 265
Monopole, equation 265
Monopole, number 266
Morphism 303
Multi-index 168
Multi-instanton solution 229
Natural transformation 307
Neighborhood 299
Non-dual 217
Normal coordinate chart 31
Normalizing constant 248
Object 303
Object, final 304
Object, inital 304
Observable 272
Odd element 315
Open covering 299
Open set 297
Operator, compact 175
Operator, differential 172
Operator, elliptic 173 174
Operator, exterior differential 16
Operator, Laplacian 178
Operator, pseudo-differential 173 174
Operator, trace class 175
Opposite path 75
Orbit 28
Orientation 14 94
Orientation system 93
Orientation system, equivalent 94
Orientation, induced 14
Outer product 184
Paracompact 300
Parallel displacement 55 64
Parallel translation 64
Parametrix 174
Partition 300
Partition function 272
Partition of unity 300
Path 75
Path connected 75
Path connected, locally 75
Pauli spin matrices 319
Pfaffian 118
Pin group 180
Poincar bundle 277
Poincar conjecture 77
Poincar conjecture, generalized 77
Poincar lemma 17
Poisson bracket 26
Polarization 116
Pontryagin class 118
Postnikov tower 85
Power set 297
Principal bundle 45
Principal bundle, automorphism 47
Principal bundle, homomorphism 47
Principal bundle, lift of 47
Principal bundle, lift of, universal 48
Principal bundle, reduced 47
Principal bundle, universal extension of 48
Principal ideal domain 309
Product manifold 7
Product topology 298
Projectable diffeomorphism 148
Projectable transformation 148
Projective space, complex 7
Projective space, quaternionic 7
Projective space, real 6
Pseudo-metric 19
Pseudo-particle solution 229
Pull-back 41
Pull-back, of a form 14
Pull-back, of a vector field 14
QCD 144
qed 141
QFT 269
Quadrupole bundles 219
Quantum chromodynamics 144
Quantum electrodynamics 141
Quantum expectation 272
Quantum field theory 272
Quantum field theory, topological 279
Quantum number 258
Quantum number, hypercharge 258
Quantum number, topological 84 123
Quantum number, weak isospin 258
Quantum observable 285
Quotient chain complex 311
Quotient manifold 11
Quotient topology 299
Rank 94
refinement 299
Regular equivalence relation 11
Regular value 10
Regularly homotopic 177
Relative  -group 132
Ricci tensor field 68
Riemann curvature 69
Right-handed fermions 258
Ring completion 130
Rochlin invariant 103
s-equivalent 132
Scalar curvature 69
Schwartz space 168
Second countable 299
Section 42
Section, harmonic 178
Section, local 42
Section, parallel 55
Sectional curvature 69
Semiclassical expectation 290
Separable 299
Shifted field 253
Short exact sequence 311
Simplex, singular 88
Simplex, singular, differentiable 96
Simplex, standard 88
Simply connected 76
Simply connected, semilocally 78
Singular chain module 89
Singular cochain module 95
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