Hamilton-Jacobi Formulation of Systems with Gauge Conditions

Khaled I. Nawafleh


After reviewing the Hamilton-Jacobi formulation approach of constrained systems using the canonical method, we apply this approach to a system of first-class constraints in the framework of the Dirac method. In constrained systems possessesing first-class constraints, some gauge conditions should be applied to convert them into second-class constraints. These conditions reduce the total Hamiltonian in Dirac’s method to the canonical one. We show that the Hamilton-Jacobi function in reduced phase space can be obtained in the same manner as for the canonical method. The equations of motion and quantization using the WKB approximation are clarified.


Hamilton-Jacobi, Constrained Systems, Gauge Conditions

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