Mangiarotti L., Sardanashvily G. — Connections in Classical and Quantum Field Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Mangiarotti L., Sardanashvily G. — Connections in Classical and Quantum Field Theory

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Название: Connections in Classical and Quantum Field Theory

Авторы: Mangiarotti L., Sardanashvily G.

Аннотация:

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 400

Добавлена в каталог: 22.10.2010

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Предметный указатель

$GH^{\infty}$ -superfunction      302
$G^{\infty}$ -superfunction      302
$G^{\infty}$ -tangent bundle      314
$G^{\infty}$ -vector bundle      313
$H^{\infty}$ -superfunction      302
$R^{\infty}$ -superfunction      306
$R^{\infty}$ -supermanifold      306
$\mathbb{Z}$ -graded algebra      451
*-left module      261
*-module      449
1-parameter group of diffeomorphisms      13
3-velocity      227
3-velocity, phase space      227
4-velocity      228
4-velocity, phase space      228
Absolute acceleration      114
Adapted coordinates      108
Adjoint representation      151
Admissible metric      233
Affine bundle coordinates      9
Affine bundle coordinates, morphism      9
Almost complex structure      204
Annihilator of a distribution      23
Anomaly      439
Anomaly, exact sequence      443
Anomaly, global      443
Anomaly, group      443
Anomaly, local      443
Antibracket      409
Antighost number      411
Antiholomorphic function      344
Associated atlas      157
Associated atlas, principal connection      158
Atiyah class      283
Atiyah — Singer connection      429
Autoparallel motion      225
Basic form      15
Basis of a graded manifold      291
Berry connection      379
Berry connection, phase factor      380
Betti number      431
Bialgebra      319
Bicomplex      399
Bimodule central      448
Body manifold      309
Body manifold of a DeWitt supermanifold      309
Body manifold of a graded manifold      290
Body manifold, map      287
Boundary      208
Boundary, relative      211
Bounded operator      372
BRS operator      327
BRST anomaly      446
BRST anomaly, cohomology      414
BRST anomaly, connection      417
BRST anomaly, operator      412
BRST anomaly, tensor field      416
BRST anomaly, total      413
BRST-closed form      427
BRST-closed form, locally      413
BRST-exact form      428
BRST-exact form of constant local trivializations      47
BRST-exact form, affine      8
BRST-exact form, associated      156
BRST-exact form, atlas      4
BRST-exact form, bundle      4
BRST-exact form, canonically      157
BRST-exact form, composite      48
BRST-exact form, coordinates      5
BRST-exact form, cotangent      10
BRST-exact form, isomorphism      5
BRST-exact form, linear      7
BRST-exact form, locally      414
BRST-exact form, morphism      5
BRST-exact form, natural      215
BRST-exact form, of principal connections      154
BRST-exact form, of world connections      217
BRST-exact form, universal      196 425
BRST-exact form, with a structure group      157
Canonical energy function      138
Canonical energy function, energy-momentum tensor      68
Canonical energy function, lift of a vector field      14
Cartan connection      46
Cartan connection, homotopy formula      437
Cech cohomology group      213
Centre of a bimodule      448
Centrifugal force      113
Chain complex      207
Chain complex, relative      210
Characteristic class      197
Characteristic class, form      197
Characteristic class, vector bundle      291
Chern character      201
Chern character of a manifold      204
Chern character, class      197
Chern character, form      198
Chern character, number      201
Chern character, total      198
Chern — Simons form      436
Chevalley-Eilenberg coboundary operator      454
Chevalley-Eilenberg coboundary operator, cochain complex      454
Chevalley-Eilenberg coboundary operator, cohomology      454
Chevalley-Eilenberg coboundary operator, differential calculus      455
Christoffel symbols      45
Classical basis      409
Classical basis, solution of a differential equation      32
Classification Theorem      196
Classifying space      196
Clifford algebra      243
Clifford algebra, group      244
Coadjoint representation      151
Coalgebra      318
Coboundary relative      211
Cochain complex      208
Cochain complex, relative      211
Cocycle      213
Cocycle, relation      4
Cocycle, relative      211
Codistribution      23
Cohomology algebra      209
Cohomology algebra with coefficients in a sheaf      213
Cohomology algebra, group      208
Cohomology algebra, relative      211
Coinverse      319
Commutant      209
Complete set of Hamiltonian forms      80
Complex canonical coordinates      356
Complex of complexes      399
Configuration space of fields      55
Connection      35
Connection on a Hermitian manifold      348
Connection on a holomorphic manifold      347
Connection on a module      269
Connection on a ring      273
Connection on a sheaf      278
Connection on an infinite order jet space      395 397
Connection principal      154
Connection principal, canonical      160
Connection, Abelian      369
Connection, admissible      353
Connection, affine      45
Connection, canonical      130
Connection, complete      94 220
Connection, composite      50
Connection, covertical      53
Connection, curvature-free      47
Connection, dual      43 52
Connection, dynamic      101
Connection, flat      47
Connection, form      155

Connection, irreducible      422
Connection, Lagrangian      61
Connection, linear      42
Connection, metric      224
Connection, projectable      49
Connection, reducible      40
Connection, second order      57
Connection, second order holonomic      58
Connection, symmetric      101
Connection, symplectic      367
Connection, tensor product      43 53
Connection, vertical      53
Connes’ differential calculus      464
Conservation law covariant      175
Conservation law covariant, integral      66
Conservation law covariant, weak      65
Contact form      26
Contact form, projection      395
Contorsion      224
Coriolis force      113
Cotangent bundle      345
Cotangent bundle, Hamiltonian vector field      349
Cotangent bundle, line bundle      199
Cotangent bundle, space      345
Cotangent bundle, structure      344
Cotangent bundle, tangent bundle      345
Cotangent bundle, tangent bundle, space      345
Covariant derivative      39
Covariant derivative, differential      39
Covariant derivative, differential on a module      270
Covariant derivative, differential vertical      51
Covariant derivative, Laplacian      423
Cup-product      209
Curvature      41
Curvature of a connection on a module      273
Curvature of a connection on a module on a sheaf      280
Curvature of a Dubois — Violette connection      459
Curvature of a graded connection      296
Curvature of a non-commutative connection      456
Curvature of a principal connection      156
Curvature of a superconnection      315
Curvature of an NQ-superconnection      338
Curvature, canonical      161
CYCLE      208
Cycle, fundamental      430
Cycle, relative      211
De Rham cohomology group      208
De Rham cohomology group, complex      208
De Rham cohomology group, complex on an infinite order jet space      393
Deformation associative      361
Deformation associative, formal      361
Democracy group      124
Derivation      259
Derivation, graded      292
Derivative left      409
Derivative left, right      409
Descent equations      414 427 446
Determinant line bundle      443
DeWitt supermanifold      308
DeWitt supermanifold, topology      308
Differential calculus      451
Differential calculus, equation      32
Differential calculus, ideal      23
Differential calculus, operator      33
Differential calculus, operator, linear      258
Differential calculus, universal      452
Dirac operator      247
Dirac operator, chiral      442
Dirac operator, spin structure      245
Dirac operator, total      252
Dirac’s condition      350
Dirac’s condition, Lagrangian      247
Direct image of a sheaf      275
Direct image of a sheaf, limit      274
Direct image of a sheaf, limit of endomorphisms      392
Direct image of a sheaf, sum connection      43
Direct image of a sheaf, system of endomorphisms      392
distribution      23
Distribution, completely integrable      23
Distribution, involutive      23
Donaldson invariant      433
Donaldson invariant, polynomials      432
Donaldson’s theorem      431
Dual Lie algebra      151
Dual vector bundle      7
Dubois — Violette connection      458
Dynamic equation      98
Dynamic equation, conservative      99
Dynamic equation, first order      32 56
Dynamic equation, second order      58
Dynamic equation, second order, autonomous      96
Energy function      138
Energy function, Hamiltonian      141
Energy-momentum current      68
Energy-momentum current, superpotential of tensor fields      237
Energy-momentum current, tensor      68
Equation of continuity      172
Equilibrium equation      135
Equivalent fibre bundles      5
Euler characteristic      206
Euler characteristic, class      205
Euler Lagrange equations      60
Euler Lagrange equations, form      402
Euler Lagrange equations, map      402
Euler Lagrange equations, operator      59
Euler Lagrange equations, operator higher order      402
Euler — Lagrange-type operator      402
Evaluation morphism      303
Exact sequence      8
Exterior algebra of a graded module      287
Exterior algebra of a graded module of a vector space      286
Exterior form      15
Exterior form, complex      345
Exterior product of vector bundles      7
External force      120
Fedosov deformation      364
Fibred manifold      4
Fibred manifold, morphism      5
Field      216
Filtered module      392
Filtered module, morphism      392
Filtered module, ring      392
First variational formula      59
First variational formula in the presence of background fields      70
First variational formula, higher order      402
Foliation      24
Foliation of level surfaces      24
Foliation, simple      24
Foliation, singular      24
Frame      7
Frame, bundle      216
Frame, connection      114
Frechet ring      267
Free motion equation      111
Froelicher — Nijenhuis bracket      20
Fubini Studi metric      350
Fundamental form of a Hermitian metric      347
Fundamental form of a Hermitian metric, group      207
Fundamental form of a Hermitian metric, vector field      152
G-function      303
G-superbundle      312
G-supermanifold      305
Galilei group      113
Gauge algebra bundle      153
Gauge algebra bundle, convention      167
Gauge algebra bundle, global      424
Gauge algebra bundle, group      167
Gauge algebra bundle, group effective      422
Gauge algebra bundle, group pointed      422
Gauge algebra bundle, parameter      167

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