Noether's Theorems: Applications in Mechanics and Field Theory

Front Cover
Springer, Mar 18, 2016 - Mathematics - 297 pages
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
 

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Contents

1 Calculus of Variations on Fibre Bundles
1
2 Noethers First Theorem
17
3 Lagrangian and Hamiltonian Field Theories
27
4 Lagrangian and Hamiltonian Nonrelativistic Mechanics
58
5 Global Kepler Problem
93
6 Calculus of Variations on Graded Bundles
103
7 Noethers Second Theorems
134
8 YangMills Gauge Theory on Principal Bundles
163
11 ChernSimons Topological Field Theory
201
12 Topological BF Theory
207
Glossary
211
Appendix ADifferential Calculus over Commutative Rings
213
Appendix BDifferential Calculus on Fibre Bundles
227
Appendix CCalculus on Sheaves
259
Appendix DNoether Identities of Differential Operators
271
References
280

9 SUSY Gauge Theory on Principal Graded Bundles
183
10 Gauge Gravitation Theory on Natural Bundles
189

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