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Marathe K.B., Martucci G. — The mathematical foundations of gauge theories
Marathe K.B., Martucci G. — The mathematical foundations of gauge theories

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Название: The mathematical foundations of gauge theories

Авторы: Marathe K.B., Martucci G.

Аннотация:

Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields.


Язык: en

Рубрика: Физика/Квантовая теория поля/Теория калибровочных полей/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 372

Добавлена в каталог: 21.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H$-space      83
$W$ boson mass      258
$W$ bosons      258
$Z^{0}$ boson      258
$Z^{0}$ boson mass      258
$\hat{A}$ 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 $C^{p}$      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, $n$-      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 $M$      65
Covariant functor      307
Covaxiant differential on $P$      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
1 2 3
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