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This volume is an introduction to differential methods in physics. Part I contains a comprehensive presentation of the geometry of manifolds and Lie groups, including infinite… Read more
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Part II: Covariant Hamiltonian Dynamics. Non-Relativistic Dynamics. Action Principle. Canonical Hamiltonian Formalism. Symplectic Manifolds and Poisson Algebras. Degenerate Lagrangians and Constraints. Cartan Equations and Symmetries. Generalized Hamiltonian Dynamics. Constraints and Reduction. Dynamics of Classical Fields. Action Principle and Field Equations. Boundary Conditions, Symmetries and Conservation Laws. Cartan Formalism in the Space of Cauchy Data. Hamiltonian Formulation. Constraints and Reduction. Yang-Mills Theory. Field Equations. Gauge Transformations and Conservation Laws. Hamiltonian Formulation. Minkowski Space. Maxwell-Dirac Theory. Yang-Mills Charges. General Relativity. Field Equations. Conservation Laws and Constraints. Hamiltonian Formulation. Asymptotically Flat Space Times. References. Index. Glossary.