A course in mathematical physics 1 and 2: Classical dynamical systems and classical field theory, Volumes 1-2
This book combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks complementing the text, it is suitable as a textbook for students of physics, mathematics, and applied mathematics. The treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems; problems discussed in detail include nonrelativistic motion of particles and systems, relativis- tic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields used differential geometry to examine both Maxwell's and Einstein's equations with new material added on gauge theories.
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Analysis on Manifolds
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algebra asymptotic bijection boundary bundle calculate canonical transformation Cauchy surface causal charge chart compact components constants of motion convergence coordinate system cosh covariant curvature curve defined Definition density depends diffeomorphism differential eigenvalues Einstein's equations electromagnetic energy energy-momentum equations of motion example exist exterior factor Figure finite flow force frequency gauge geodesic global gravitational field Green function Hamiltonian Hence implies independent infinite infinity integral interior product Killing vector fields Lagrangian Lie derivative linear Lorentz Lorentz transformation manifold mapping mathematical matrix Maxwell's equations metric Minkowski space natural basis orbits orthogonal basis oscillator particle phase space Poisson brackets potential Problem pseudo-Riemannian radiation region relativistic Remarks restriction Riemannian rotating satisfies scalar product Schwarzschild Schwarzschild metric Show singularity solution spacelike structure submanifold subset surface tangent tensor field term theorem theory time-evolution Tq(M trajectories vanish variables velocity wave zero