Advanced classical field theory:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
New Scientific
[2009]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 382 Seiten |
| ISBN: | 9789812838957 9812838953 |
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MARC
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| 100 | 1 | |a Giachetta, G. |d 1961-2014 |e Verfasser |0 (DE-588)1192332954 |4 aut | |
| 245 | 1 | 0 | |a Advanced classical field theory |c Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| 264 | 1 | |a New Jersey |b New Scientific |c [2009] | |
| 300 | |a x, 382 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Field theory (Physics) |x Mathematics | |
| 650 | 4 | |a Lagrange equations | |
| 650 | 0 | 7 | |a Feldtheorie |0 (DE-588)4016698-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Mangiarotti, Luigi |e Verfasser |0 (DE-588)141878053 |4 aut | |
| 700 | 1 | |a Sardanašvili, Gennadij A. |d 1950- |e Verfasser |0 (DE-588)14187810X |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018615097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018615097 | ||
Record in the Search Index
| _version_ | 1804140675646619648 |
|---|---|
| adam_text | Contents
Preface
v
Introduction
1
1.
Differential calculus on fibre bundles
5
1.1
Geometry of fibre bundles
.................. 5
1.1.1
Manifold morphisms
................. 6
1.1.2
Fibred manifolds and fibre bundles
........ 7
1.1.3
Vector and
affine
bundles
.............. 12
1.1.4
Vector fields, distributions and foliations
..... 18
1.1.5
Exterior and tangent-valued forms
......... 21
1.2
Jet manifolds
......................... 26
1.3
Connections on fibre bundles
................ 29
1.3.1
Connections as tangent-valued forms
....... 30
1.3.2
Connections as jet bundle sections
......... 32
1.3.3
Curvature and torsion
................ 34
1.3.4
Linear connections
.................. 36
1.3.5 Affine
connections
.................. 38
1.3.6
Flat connections
................... 39
1.3.7
Second order connections
.............. 41
1.4
Composite bundles
...................... 42
1.5
Higher order jet manifolds
.................. 46
1.6
Differential operators and equations
............ 51
1.7
Infinite order jet formalism
................. 54
2.
Lagrangian field theory on fibre bundles
61
2.1
Variational bicomplex
.................... 61
YÜi Contents
2.2
Lagrangian symmetries
.................... 66
2.3
Gauge symmetries
...................... 70
2.4
First order Lagrangian field theory
............. 73
2.4.1
Cartan and Hamilton-De
Donder
equations
... 75
2.4.2
Lagrangian conservation laws
............ 78
2.4.3
Gauge conservation laws.
Superpotential
..... 80
2.4.4
Non-regular quadratic Lagrangians
........ 83
2.4.5
Reduced second order Lagrangians
......... 87
2.4.6
Background fields
.................. 88
2.4.7
Variation Euler-Lagrange equation. Jacobi fields
. 90
2.5
Appendix. Cohomology of the variational bicomplex
... 92
3.
Grassmann-graded Lagrangian field theory
99
3.1
Grassmann-graded algebraic calculus
............ 99
3.2
Grassmann-graded differential calculus
........... 104
3.3
Geometry of graded manifolds
................ 107
3.4
Grassmann-graded variational bicomplex
.......... 115
3.5
Lagrangian theory of even and odd fields
.......... 120
3.6
Appendix. Cohomology of the Grassmann-graded varia¬
tional bicomplex
....................... 125
4.
Lagrangian
BRST
theory
129
4.1
Noether identities. The Koszul-Tate complex
....... 130
4.2
Second Noether theorems in a general setting
....... 140
4.3
BRST
operator
........................ 147
4.4
BRST
extended Lagrangian field theory
.......... 150
4.5
Appendix. Noether identities of differential operators
. . . 154
5.
Gauge theory on principal bundles
165
5.1
Geometry of Lie groups
................... 165
5.2
Bundles with structure groups
............... 169
5.3
Principal bundles
....................... 171
5.4
Principal connections. Gauge fields
............. 175
5.5
Canonical principal connection
............... 179
5.6
Gauge transformations
.................... 181
5.7
Geometry of associated bundles. Matter fields
....... 184
5.8
Yang-Mills gauge theory
................... 188
5.8.1
Gauge field Lagrangian
............... 188
Contents jx
5.8.2
Conservation
laws
.................. 190
5.8.3
BRST
extension
................... 192
5.8.4
Matter field Lagrangian
............... 194
5.9
Yang-Mills supergauge theory
................ 196
5.10
Reduced structure. Higgs fields
............... 198
5.10.1
Reduction of a structure group
........... 198
5.10.2
Reduced subbundles
................. 200
5.10.3
Reducible principal connections
.......... 202
5.10.4
Associated bundles. Matter and Higgs fields
. . . 203
5.10.5
Matter field Lagrangian
............... 207
5.11
Appendix. Non-linear realization of Lie algebras
..... 211
6.
Gravitation theory on natural bundles
215
6.1
Natural bundles
........................ 215
6.2
Linear world connections
................... 219
6.3
Lorentz
reduced structure. Gravitational field
....... 223
6.4
Space-time structure
..................... 228
6.5
Gauge gravitation theory
.................. 232
6.6
Energy-momentum conservation law
............ 236
6.7
Appendix.
Affine
world connections
............ 238
7.
Spinor fields
243
7.1
Clifford algebras and Dirac spinors
............. 243
7.2
Dirac spinor structure
.................... 246
7.3
Universal spinor structure
.................. 252
7.4
Dirac fermion fields
...................... 258
8.
Topological field theories
263
8.1
Topological characteristics of principal connections
.... 263
8.1.1
Characteristic classes of principal connections
. . 264
8.1.2
Flat principal connections
............. 266
8.1.3
Chern classes of unitary principal connections
. . 270
8.1.4
Characteristic classes of world connections
.... 274
8.2
Chem-Simons topological field theory
........... 278
8.3
Topological BF theory
.................... 283
8.4
Lagrangian theory of submanifolds
............. 286
9.
Covariant Hamiltonian field theory
293
x
Contents
9.1 Polysymplectic Hamiltonian
formalism............
293
9.2 Associated Hamiltonian
and Lagrangian systems
..... 298
9.3 Hamiltonian
conservation laws ...............
304
9.4
Quadratic
Lagrangian
and Hamiltonian systems
...... 306
9.5
Example, Yang-Mills gauge theory
............. 313
9.6
Variation Hamilton equations. Jacobi fields
........ 316
10.
Appendixes
319
10.1
Commutative algebra
.................... 319
10.2
Differential operators on modules
.............. 324
10.3
Homology and cohomology of complexes
.......... 327
10.4
Cohomology of groups
.................... 330
10.5
Cohomology of Lie algebras
................. 333
10.6
Differential calculus over a commutative ring
....... 334
10.7
Sheaf cohomology
....................... 337
10.8
Local-ringed spaces
...................... 346
10.9
Cohomology of smooth manifolds
.............. 348
10.10
Leafwise and fibrewise cohomology
............. 354
Bibliography
359
Index
369
|
| any_adam_object | 1 |
| author | Giachetta, G. 1961-2014 Mangiarotti, Luigi Sardanašvili, Gennadij A. 1950- |
| author_GND | (DE-588)1192332954 (DE-588)141878053 (DE-588)14187810X |
| author_facet | Giachetta, G. 1961-2014 Mangiarotti, Luigi Sardanašvili, Gennadij A. 1950- |
| author_role | aut aut aut |
| author_sort | Giachetta, G. 1961-2014 |
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| dewey-full | 530.12 |
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| dewey-ones | 530 - Physics |
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| dewey-search | 530.12 |
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035755119 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:45Z |
| institution | BVB |
| isbn | 9789812838957 9812838953 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018615097 |
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| owner_facet | DE-355 DE-BY-UBR DE-11 DE-384 DE-20 |
| physical | x, 382 Seiten |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | New Scientific |
| record_format | marc |
| spelling | Giachetta, G. 1961-2014 Verfasser (DE-588)1192332954 aut Advanced classical field theory Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily New Jersey New Scientific [2009] x, 382 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematik Field theory (Physics) Mathematics Lagrange equations Feldtheorie (DE-588)4016698-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 s DE-604 Mangiarotti, Luigi Verfasser (DE-588)141878053 aut Sardanašvili, Gennadij A. 1950- Verfasser (DE-588)14187810X aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018615097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Giachetta, G. 1961-2014 Mangiarotti, Luigi Sardanašvili, Gennadij A. 1950- Advanced classical field theory Mathematik Field theory (Physics) Mathematics Lagrange equations Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4016698-3 |
| title | Advanced classical field theory |
| title_auth | Advanced classical field theory |
| title_exact_search | Advanced classical field theory |
| title_full | Advanced classical field theory Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_fullStr | Advanced classical field theory Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_full_unstemmed | Advanced classical field theory Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_short | Advanced classical field theory |
| title_sort | advanced classical field theory |
| topic | Mathematik Field theory (Physics) Mathematics Lagrange equations Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Mathematik Field theory (Physics) Mathematics Lagrange equations Feldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018615097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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