Classical Mathematical Physics: Dynamical Systems And Field Theories - Brossura

Harrell, E.M.

Brossura

ISBN 10: 0387406158 ISBN 13: 9780387406152

Casa editrice: Springer, 2013

Riassunto

This volume 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 accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.

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Recensione:

From the reviews:

"... A complete book in classical field theory. Moreover it is very interesting to see the geometry of relativity. I highly recommend this book for the theoretical physicists and mathematicians interested in physics. In short this is a very useful book."  H. Cebeci, Middle East Technical University, Ankara, Turkey

Contenuti:

I Classical Dynamical Systems.- 1 Introduction.- 1.1 Equations of Motion.- 1.2 The Mathematical Language.- 1.3 The Physical Interpretation.- 2 Analysis on Manifolds.- 2.1 Manifolds.- 2.2 Tangent Spaces.- 2.3 Flows.- 2.4 Tensors.- 2.5 Differentiation.- 2.6 Integrals.- 3 Hamiltonian Systems.- 3.1 Canonical Transformations.- 3.2 Hamilton’s Equations.- 3.3 Constants of Motion.- 3.4 The Limit t ? ±?.- 3.5 Perturbation Theory: Preliminaries.- 3.6 Perturbation Theory: The Iteration.- 4 Nonrelativistic Motion.- 4.1 Free Particles.- 4.2 The Two-Body Problem.- 4.3 The Problem of Two Centers of Force.- 4.4 The Restricted Three-Body Problem.- 4.5 The N-Body Problem.- 5 Relativistic Motion.- 5.1 The Hamiltonian Formulation of the Electrodynamic Equations of Motion.- 5.2 The Constant Field.- 5.3 The Coulomb Field.- 5.4 The Betatron.- 5.5 The Traveling Plane Disturbance.- 5.6 Relativistic Motion in a Gravitational Field.- 5.7 Motion in the Schwarzschild Field.- 5.8 Motion in a Gravitational Plane Wave.- 6 The Structure of Space and Time.- 6.1 The Homogeneous Universe.- 6.2 The Isotropic Universe.- 6.3 Me According to Galileo.- 6.4 Me as Minkowski Space.- 6.5 Me as a Pseudo-Riemannian Space.- II Classical Field Theory.- 7 Introduction to Classical Field Theory.- 7.1 Physical Aspects of Field Dynamics.- 7.2 The Mathematical Formalism.- 7.3 Maxwell’s and Einstein’s Equations.- 8 The Electromagnetic Field of a Known Charge Distribution.- 8.1 The Stationary-Action Principle and Conservation Theorems.- 8.2 The General Solution.- 8.3 The Field of a Point Charge.- 8.4 Radiative Reaction.- 9 The Field in the Presence of Conductors.- 9.1 The Superconductor.- 9.2 The Half-Space, the Wave-Guide, and the Resonant Cavity.- 9.3 Diffraction at a Wedge.- 9.4 Diffraction at a Cylinder.- 10 Gravitation.- 10.1 Covariant Differentiation and the Curvature of Space.- 10.2 Gauge Theories and Gravitation.- 10.3 Maximally Symmetric Spaces.- 10.4 Spaces with Maximally Symmetric Submanifolds.- 10.5 The Life and Death of Stars.- 10.6 The Existence of Singularities.

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2013
• ISBN 10: 0387406158
• ISBN 13: 9780387406152
• Rilegatura: Copertina flessibile
• Numero edizione: 3
• Numero di pagine: 576