Noether's Theorems: Applications in Mechanics and Field Theory

ISBN-13: 9789462391703 / Angielski / Twarda / 2016 / 297 str.

Gennadi Sardanashvily

Opis

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.

Recenzje

"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)

Spis treści

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.