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 bre bundles.- Noethers rst theorem.- Lagrangian and Hamiltonian eld theories.- Lagrangian and Hamiltonian nonrelativistic mechanics.- Global Kepler problem.- Calculus of variations on graded bundles.- Noethers 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. This book contains a systematic and detailed approach to Lagrangian systems through the variational bicomplex providing a very general geometric and algebraic view of the variational calculus. & The book is very well written in a clear and direct style containing very helpful cross references. In addition the book under review includes 4 appendices which make the presentation self contained. (Miguel Paternain, zbMATH 1357.58002, 2017)
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 LagrlsK
![Noether's Theorems: Applications in Mechanics and Field Theory [Hardcover]](/itemImage/2/0/5/2/2_1016659.jpg "Noether's Theorems: Applications in Mechanics and Field Theory [Hardcover]")