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.
Rezensionen / Stimmen
"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)
Reihe
Sprache
Verlagsort
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Dateigröße
ISBN-13
978-94-6239-171-0 (9789462391710)
DOI
10.2991/978-94-6239-171-0
Schweitzer Klassifikation
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.- Yang-Mills gauge theory on principal bundles.- SUSY gauge theory on principal graded bundles.- Gauge gravitation theory on natural bundles.- Chern-Simons topological ?eld theory.- Topological BF theory.
