Noether Theorems Applications in Mechanics and Field Theory 1st Edition by Gennadi Sardanashvily ISBN 9462391718 9789462391710

1 Calculus of Variations on Fibre Bundles

1.1 Infinite Order Jet Formalism

1.2 Variational Bicomplex

1.3 Lagrangian Formalism

2 Noether’s First Theorem

2.1 Lagrangian Symmetries

2.2 Gauge Symmetries: Noether’s Direct Second Theorem

2.3 Noether’s First Theorem: Conservation Laws

3 Lagrangian and Hamiltonian Field Theories

3.1 First Order Lagrangian Formalism

3.2 Cartan and Hamilton–De Donder Equations

3.3 Noether’s First Theorem: Energy-Momentum Currents

3.4 Conservation Laws in the Presence of a Background Field

3.5 Covariant Hamiltonian Formalism

3.6 Associated Lagrangian and Hamiltonian Systems

3.7 Noether’s First Theorem: Hamiltonian Conservation Laws

3.8 Quadratic Lagrangian and Hamiltonian Systems

4 Lagrangian and Hamiltonian Nonrelativistic Mechanics

4.1 Geometry of Fibre Bundles over mathbbR

4.2 Lagrangian Mechanics. Integrals of Motion

4.3 Noether’s First Theorem: Energy Conservation Laws

4.4 Gauge Symmetries: Noether’s Second and Third Theorems

4.5 Non-autonomous Hamiltonian Mechanics

4.6 Hamiltonian Conservation Laws: Noether’s Inverse First Theorem

4.7 Completely Integrable Hamiltonian Systems

5 Global Kepler Problem

6 Calculus of Variations on Graded Bundles

6.1 Grassmann-Graded Algebraic Calculus

6.2 Grassmann-Graded Differential Calculus

6.3 Differential Calculus on Graded Bundles

6.4 Grassmann-Graded Variational Bicomplex

6.5 Grassmann-Graded Lagrangian Theory

6.6 Noether’s First Theorem: Supersymmetries

7 Noether’s Second Theorems

7.1 Noether Identities: Reducible Degenerate Lagrangian Systems

7.2 Noether’s Inverse Second Theorem

7.3 Gauge Supersymmetries: Noether’s Direct Second Theorem

7.4 Noether’s Third Theorem: Superpotential

7.5 Lagrangian BRST Theory

8 Yang–Mills Gauge Theory on Principal Bundles

8.1 Geometry of Principal Bundles

8.2 Principal Gauge Symmetries

8.3 Noether’s Direct Second Theorem: Yang–Mills Lagrangian

8.4 Noether’s First Theorem: Conservation Laws

8.5 Hamiltonian Gauge Theory

8.6 Noether’s Inverse Second Theorem: BRST Extension

9 SUSY Gauge Theory on Principal Graded Bundles

10 Gauge Gravitation Theory on Natural Bundles

10.1 Relativity Principle: Natural Bundles

10.2 Equivalence Principle: Lorentz Reduced Structure

10.3 Metric-Affine Gauge Gravitation Theory

10.4 Energy-Momentum Gauge Conservation Law

10.5 BRST Gravitation Theory

11 Chern–Simons Topological Field Theory

12 Topological BF Theory