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.
Chapter 1 Calculus of Variations on Fibre Bundles
Chapter 2 Noether’s First Theorem
Chapter 3 Lagrangian and Hamiltonian Field Theories
Chapter 4 Lagrangian and Hamiltonian Nonrelativistic Mechanics
Chapter 5 Global Kepler Problem
Chapter 6 Calculus of Variations on Graded Bundles
Chapter 7 Noether’s Second Theorems
Chapter 8 Yang–Mills Gauge Theory on Principal Bundles
Chapter 9 SUSY Gauge Theory on Principal Graded Bundles
Chapter 10 Gauge Gravitation Theory on Natural Bundles
Chapter 11 Chern–Simons Topological Field Theory
Chapter 12 Topological BF Theory
Appendix A Differential Calculus over Commutative Rings
Appendix B Differential Calculus on Fibre Bundles
Appendix C Calculus on Sheaves
Appendix D Noether Identities of Differential Operators
