تئوری‌های نوتر: کاربردها در مکانیک و نظریه میدان (مطالعات آتلانتیس در هندسه واریاسیون، جلد سوم)

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. Front Matter....Pages i-xvii Calculus of Variations on Fibre Bundles....Pages 1-15 Noether’s First Theorem....Pages 17-25 Lagrangian and Hamiltonian Field Theories....Pages 27-57 Lagrangian and Hamiltonian Nonrelativistic Mechanics....Pages 59-92 Global Kepler Problem....Pages 93-101 Calculus of Variations on Graded Bundles....Pages 103-133 Noether’s Second Theorems....Pages 135-161 Yang–Mills Gauge Theory on Principal Bundles....Pages 163-181 SUSY Gauge Theory on Principal Graded Bundles....Pages 183-188 Gauge Gravitation Theory on Natural Bundles....Pages 189-200 Chern–Simons Topological Field Theory....Pages 201-206 Topological BF Theory....Pages 207-210 Back Matter....Pages 211-297