Classical Field Theory in the Hamilton-Jacobi Formalism

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Abstract
A Hamilton-Jacobi formalism of classical relativistic field theory is developed. Both "time-independent" and "time-dependent" formulations are given, and the relation between them is discussed. In the former, the constants of the motion are identified with the "new" field variables, whereas in the latter they are the values of the fields on a suitable spacelike surface. The explicit introduction of a Hamiltonian density is avoided. As an illustration of the respective procedures, the classical Dirac and Klein-Gordon free fields are solved explicitly. A perturbation method is formulated for the case of fields in interaction. The metric tensor is not treated as a field quantity.

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