Noether's Theorems

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.

Noether's theorems are presented in the most general and universal form The calculus of variations and Lagrangian theory are formulated in a very general setting Relevant examples from mechanics and field theory help the reader to understand the general theory of Noether's theorems and their applications in physics Includes supplementary material: sn.pub/extras

Contenu
Calculus of variations on bre bundles.- Noether's rst theorem.- Lagrangian and Hamiltonian eld theories.- Lagrangian and Hamiltonian nonrelativistic mechanics.- Global Kepler problem.- Calculus of variations on graded bundles.- Noether's second theorems.- YangMills gauge theory on principal bundles.- SUSY gauge theory on principal graded bundles.- Gauge gravitation theory on natural bundles.- ChernSimons topological eld theory.- Topological BF theory.