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Bleecker D. — Gauge Theory and Variational Principles
Bleecker D. — Gauge Theory and Variational Principles

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Название: Gauge Theory and Variational Principles

Автор: Bleecker D.

Аннотация:

Detailed and self-contained, this text supplements its rigor with intuitive ideas and is geared toward beginning graduate students and advanced undergraduates. Topics include principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 179

Добавлена в каталог: 10.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration      142
action      55
Action density      53
Action, self      68
Adjoint actions      20
Automorphisms of PFBs      46
Base manifold      26
Bianchi identity      39
Bianchi identity, first      115
Bianchi identity, second      115
Broken Hessian      157
Canonica 1-form      78
Characteristic classes      164
Charge density      16
Chart      7
Chern — Weil homomorphism      162
Choice of gauge      26
Clifford algebra      82
Closed form      15
Codifferential      14
Compact subset      11
Connection      29—31
Conservation law, charge      17 67
Conservation law, energy-momentum      127
Conservation law, external      132
Continuity equation      17 67
Contraction of tensors      109
Coordinate system      7
Coordinate vector fields      8
Covariant codifferential      58
Covariant derivative      37 111 142
Critical point      18
Current      65—66
Current for E-M      16
Curvature      see also “Riemann — Christoffel curvature
Curvature as field strength      37 39
Curvature of connection      37
Curve      8
de Rham cohomology space      15
Diffeomorphism      7
Differential of map      8
Dirac equation, free      87
Dirac equation, nonfree      98
Dirac matrices      81
Divergence      125 127
Duality for 2-forms      168
Einstein field equation      127 134
Einstein tensor      127
electric field      16 145
electromagnetic field      33 145
Electron field      83 96
Exact form      15
Exponential map      19 48
Exterior derivative      11
Exterior derivative, covariant      37 44
Fiber      26
Fiber derivative      156
Field equation, Einstein      127 134
Field equation, homogeneous      39
Field equation, inhomogeneous      68 94 98 103—104
Field strength      37 39
Forms, equivariant      44
Forms, real-valued      10
Forms, vector-valued      17
Frame bundle      28 78
Fundamental field      30
Gauge algebra      48
Gauge orbit      151
Gauge potentials      33
Gauge transformations      46
Gauge unitary      157
Gauge, choice of      26
Gauss — Bonnet theorem      126
Geodesic      142
Global section      27
Global trivialization      27
Goldstone bosons      156
Graded Lie algebra      36
Gradient of metric functional      123—124
hessian      18
Hessian broken      157
Higgs fields      156
Horizontal lift of curve      141
Horizontal lift of vector field      37
instantons      168—169
Integration of forms      11—12
Isospin current      101—102
Jacobi identity      8
Jets      50 93 148
L-tensors      107
L-tensors components      108—109
L-tensors contraction      109
L-tensors raising and lowering indices      112
L-tensors, covariant differentiation of      111
L-tensors, tensor product      109
Lagrange's equation      61 94
Lagrangian connection      148
Lagrangian curvature      152
Lagrangian electron      83 96
Lagrangian G-invariant      51
Lagrangian nucleon      99—100
Lagrangian particle field      50
Lagrangian spin-zero      62
Left-invariant vector field      18
Levi-Civita connection      77 110
Lie algebra      18
Lie derivative      9 131
Lie group      18
Lie subgroup      19
Local section      27
Local trivialization      26
Lorentz group      73
Magnetic field      16 145
Magnetic monopoles      166—168
Manifold      7
MAP      7
Mass of Higgs field      156
Massive vector bosons      158—160
Maxwell's equations      16—17 63
Metric on manifold      14
Metric on vector space      3
Minkowski space      16
Nucleon field      99
Nucleon field equation      103—105
One-parameter group      9
Open covering      11
Open subset      6
Orientation      3 11 81
Orthonormal frame bundle      78
Parallel translation      142
Particle fields      43
Principal fiber bundles      26
Principle of least action for metrics      123
Principle of least action for metrics with connections      134
Principle of least action for particle fields      56
Principle of least action for particle fields with connections      68
Product bundle      26—27
Product manifold      17
Projected support      56
Pull-back      11 127
Representation      43
Ricci identity      119
Ricci tensor      116
Riemann — Christoffel curvature tensor      114
Riemann — Christoffel curvature tensor, identities      115
Riemann — Christoffel curvature tensor, infinitesimal changes      118—119
Scalar curvature      116
Scalar mesons      156
Self-action      68
Shifted field      156
Source 1-form      16; see also “Current”
Special unitary group      21—22
Spin structure      81
Spin-zero electrodynamics      62 70
Spinors      76—77
Spliced bundles      90
Spontaneous symmetry breaking      154— 160
Standard horizontal fields      110
Star operators      4 14 56
Stationary metric      123
Stationary metric with connection      134
Stationary particle fields      56
Stationary particle fields with connection      68
Stokes' theorem      12
Structural equations      37 80
Structure constants      21
Submanifold      16
Submersion      149
Support      11
Tangent vector      8
Tensor field      10
Tensor product      109
Torsion form      78
Total space      26
Transition function      27
Trivial bundle      27
Twisted metric      82
Unbroken subgroup      154
Unitary gauge      157
Unitary set      157
Utiyama's theorem      153
VACUUM      154
Vector field      8
Vector-valued forms      17
Vertical subspace      29
Volume element      3 14
Wedge product      3
Weil algebra      161
Weil polynomial      153 161
Yang — Mills equation      65 134
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