Noether's Theorems, 1st ed. 2016 Applications in Mechanics and Field Theory Atlantis Studies in Variational Geometry Series, Vol. 3

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.

Calculus of variations on fibre bundles.- Noether’s first theorem.- Lagrangian and Hamiltonian field theories.- Lagrangian and Hamiltonian nonrelativistic mechanics.- Global Kepler problem.- Calculus of variations on graded bundles.- Noether’s second theorems.- Yang–Mills gauge theory on principal bundles.- SUSY gauge theory on principal graded bundles.- Gauge gravitation theory on natural bundles.- Chern–Simons topological field theory.- Topological BF theory.