Articoli correlati a A Course in Mathematical Physics 2: Classical Field...
Sinossi
This volume presents the classical theory of fields with the methods of modern differential geometry. This approach not only has conceptual advantages, but is also technically convenient for the solution of Maxwell's and Einstein's equations: Cartan's formalism sweeps away the jumble of indices and allows the geometrical meaning of the observables to emerge. The need to accommodate all the material in a one-semester course and the desirability of a concise presentation have necessitated a drastic selection of topics; many an expert with a pet topic will no doubt be reluctant to forgive my sins of omission. Continuing in the spirit of the first volume, I have attempted to introduce only what can strictly be deduced from first principles. Those parts of the theory described by W. Pauli as "wishful mathematics" are left out. In order that this selection does not leave the material sterile, intuitive arguments are also presented, with the help of which many' of the mathematical intricacies in the more complicated problems can be glossed over. Classical field theory almost attains the ideal of a complete, deductive theory, but not quite. Occasionally the singularity of a l/r potential causes difficulties for electrodynamics as well as for gravitation. This seems to be a characteristic of all physical theories; although they may encompass large portions of our knowledge, a small kernel of incompleteness is inevitably left.
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