Noether's theorems [electronic resource] : applications in mechanics and field theory /
Sardanashvily, Gennadi.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Global analysis (Mathematics).
Manifolds (Mathematics).
Mechanics.
Mathematical physics.
Global Analysis and Analysis on Manifolds.
Classical Mechanics.
Mathematical Applications in the Physical Sciences.