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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.
In contrast with quantum theory, classical field theory can be
formulated in a strict mathematical way by treating classical
fields and dynamic variables as sections of smooth fiber bundles.
This book aims to compile the relevant material on fiber bundles,
jet manifolds, connections, graded manifolds and Lagrangian theory.
The book is based on the graduate and post graduate courses of
lectures given at the Department of Theoretical Physics of Moscow
State University (Russia). It addresses to a wide audience of
mathematicians, mathematical physicists and theoreticians.
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