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| Marathe K.B., Martucci G. — The mathematical foundations of gauge theories |
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| Предметный указатель |
 -space 83
 boson mass 258
bosons 258
 boson 258
boson mass 258
 genus 121
Action, adjoint 31
Action, effective 29
Action, fiber-transitive 262
Action, free 29
Action, transitive 28
ADHM construction 230
Adjoint 175
Adjoint representation of a Lie algebra 32
Adjoint representation of a Lie group 31
Adjunction space 104
Alexander polynomial 284
Anomaly 289
Anti-instanton 225
Anti-instanton, complex 237
Anti-instanton, deformation complex 237
Anti-instanton, equation 215 225
Asthenons 261
Atlas 2
Atlas, differentiable 2
Atlas, differential 2
Atlas, finite 3
Atlas, of class  2
Atlas, smooth 2
Atlas, with boundary 4
Attaching map 104
Autoparallel curve 70
Autoparallel vector field 70
Ball 298
Base 299
Betti number 95
Bianchi identity 60 65 249
Bogomolnyi equations 265
Bohm — Aharonov effect 209
Boson 141
Bott class 184
Bott homomorphism 125
Bott periodicity 86
Bott periodicity, theorem 87 184
Boundary 4 310
Boundary operator 309
Boundary, relative 92
Bracket of forms 23 154
Bracket of vector fields 9
BRST 274
Bundle, base space of 40
Bundle, horizontal 54 71
Bundle, morphism 41
Bundle, of frames 46
Bundle, of orthonormal frames 47
Bundle, projection 40
Bundle, space 40
Bundle, tautological 62
Bundle, total space of 40
Bundle, trivial 40
Bundle, vertical 54 71
Canonical 1-form 24
Canonical coordinate system 24 25
Category 303
Chain 309
Chain complex 309
Chain complex, exact 310
Chain complex, relative singular 92
Chain complex, singular 90
Chain morphism 310
Chain, elementary singular 89
Chain, singular 89
Characteristic class, complex 117
Characteristic class, primaxy 123
Characteristic class, real 117
Characteristic class, simple secondary 126
Charge operator 256
Chart 2
Chart, positively oriented 14
Chart, symplectic 25
Chart, with boundary 4
Chern character 120
Chern class 119
Chern class, total 120
Chern polynomial 120
Chern — Simons action 279
Chern — Simons class 127
Chern — Simons theory 279
Chern — Weil homomorphism 117
Christoffel symbols 66
Classifying property 108
Classifying space, universal 109 124
Clifford algebra 316
Clifford bundle 181
Clifford map 316
Closed 299
Closure 299
Coadjoint representation 32
Cobordant manifolds 114
Cobordism group 114
Coboundary 95 312
Coboundaxy operator 95 312
Cochain complex 312
Cochain complex, total 313
Cocycle 95 312
Cocycle condition 41
Codifferential 21
Cohomology algebra 110
Cohomology module 312
Cohomology module, singular 95
Cohomology module, singular, with compact support 96
Cohomology ring 110
Commutator 9
Compact 299
Complement 10
Complemented subspace 10
Complex scalax field 252
Configuration space 189
Configuration space, Yang — Mills — Higgs 248
Conformal trasformation 191
Conjugate momenta 25
Connected 300
Connected components 300
Connected,  - 76
Connected, 0- 76
Connected, 1- 76
Connecting morphisms 312
Connection 54 57-58
Connection form 57
Connection, canonical 263
Connection, gauge equivalent 156
Connection, invariant 262
Connection, linear 66
Connection, locally invariant 264
Connection, Riemannian 69
Connection, symmetry group of 264
Connection, torsion free 67
Connection, universal 62
Continuous function 298
Contractible 75
Contravariant functor 307
Cosmological constant 193
Cotangent space 13
Coupling constant 248
Coupling constant, gauge 255
Coupling constant, Yukawa 250
Covariant derivative 64
Covariant differential on  65
Covariant functor 307
Covaxiant differential on  59
| Cover 299
Covering 77-78 299
Covering group, universal 80
Covering projection 77
Covering space 77
Covering space, universal 78
Curl 22
Curvature 60
Curvature product 194
Curvature, tensor field 68
CYCLE 310
Cycle, relative 92
Darboux’s theorem 25
Deck transformation 78
Dense 299
deRham cohomology 97
deRham complex 97
DeRham homomorphism 97
Diffeomorphism 3
Differential complex 177
Differential structure 2
Dirac bundle 183
Dirac monopole 146
Dirac operator 182
Dirac operator, twisted 237
Direct limit 306
Direct system 306
Directed set 306
disconnection 300
Disk bundle 114
Distance function 298
distribution 45
Divergence 22
Donaldson polynomials 286
Dual cochain complex 313
Eilenberg — MacLane space 85
Einstein manifold 70
Einstein tensor 193
Electric displacement 204
Electroweak gauge group 258
Electroweak theory 254
Elliptic complex 178
Embedding 12
Equivariant 47
Euler chaxacteristic 95
Euler class 112 119
Even element 315
Excision 93
Excision property 93
Exponential mapping 31
Exterior algebra 13
Exterior product 305
Extreme Value Theorem 300
Face 89
Fermion 141
Fiber 40
Fiber bundle 40
Fiber bundle, associated 50
Fiber bundle, principal 45
Fiber bundle, with structure group 43
First countable 299
First Gribov horizon 164
Flat bundle 281
Flat connection 281
Flat connection, deformation complex 281
Floer homology groups 284
FORM 13
Form, associated 59
Form, bundle valued 43
Form, bundle valued, anti-dual 214
Form, bundle valued, anti-dual part 215
Form, bundle valued, self-dual 214
Form, bundle valued, self-dual part 214
Form, closed 17
Form, coclosed 21
Form, coexact 21
Form, energy of 45
Form, exact 17
Form, harmonic 98
Form, norm of 45
Form, vector valued 43
Form, vector valued, horizontal 59
Form, vector valued, pseudo-tensorial 59
Form, vector valued, tensorial 59
Fourier transform 168
Frame 46
Fredholm operator 175
Freudenthal suspension homomorphism 84
Function, differentiable 3
Function, representative of 3
Function, smooth 3
Function, tangent of 10
Fundamental class 94
Fundamental group 76
Gauge 146
Gauge connection 146
Gauge connection, form 146
Gauge connections, space of 152
Gauge field on the base 146
Gauge field on the bundle 146
Gauge group 145
Gauge group, color 142
Gauge group, electroweak 143
Gauge group, weak hypercharge 143
Gauge group, weak isospin 143
Gauge potential 146
Gauge potential, local 146
Gauge potentials, moduli space of 156
Gauge potentials, space of 152
Gauge transformation, large 280
Gauge transformations, group of 149
Gauge transformations, group of based 158
Gauge transformations, group of effective 158
Gauge transformations, group of generalized 148
Gauge transformations, restricted group of 158
Gauge transformations, small 280
Gauge, algebra 151
Gauge, global 146
Gauge, local 146
Gell — Mann — Nishijima relation 259
Generalized field equations 194
Generalized zeta function 291
Geodesic 70
Gluons 144
Goldstone boson 253
Goldstone’s theorem 254
Graded algebra 315
Graded transformation 315
Graded vector space 315
Graded vector space, element of 315
Graded vector space, element of, degree 315
Graded vector space, element of, even 315
Graded vector space, element of, odd 315
Gradient 22
Grassmann manifold 7 61
Gravitational field 193
Gravitational field, generalized 196
Gravitational tensor 196
Graviton 143
Gribov ambiguity 160
Gribov region 164
Grothendieck group 129
Grothendieck group, reduced 133
Grothendieck ring 130
Grothendieck ring, reduced 131
Ground state 252
Group, complex symplectic 36
Group, general linear 8
Group, orthogonal 27 33
Group, quaternionic symplectic 37
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