Noether's Theorems

Applications in Mechanics and Field Theory

Gennadi Sardanashvily

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English

Atlantis Press (Zeger Karssen)
16 March 2016

Calculus of variations; Mathematical physics

Series: Atlantis Studies in Variational Geometry

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.

By: Gennadi Sardanashvily
Imprint: Atlantis Press (Zeger Karssen)
Edition: 2016 ed.
Volume: 3
Dimensions: Height: 235mm, Width: 155mm, Spine: 19mm
Weight: 5.974kg
ISBN: 9789462391703
ISBN 10: 946239170X
Series: Atlantis Studies in Variational Geometry
Pages: 297
Publication Date: 16 March 2016
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Noether's Theorems: Applications in Mechanics and Field 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)