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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
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, $n$-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$\ddot{u}$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, $n$-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, $L^{2}$ 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$\acute{e}$ bundle      277
Poincar$\acute{e}$ conjecture      77
Poincar$\acute{e}$ conjecture, generalized      77
Poincar$\acute{e}$ 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 $K$-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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