Hamiltonian formulation of a theory with constraints

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Abstract
The Hamiltonian formulation of a constrained dynamical system with four degrees of freedom, the quantization of which has recently been discussed by Hojman and Shepley [J. Math. Phys. 32, 142 (1991)], is considered. The theory possesses four primary constraints which are all second class. The system is quantized using the Dirac’s procedure. Next the theory is reduced to the three-dimensional one by setting q4=k=const. It is found that the theory now possesses only three primary constraints which are all first class; and consequently the theory now becomes a gauge theory. This three-dimensional theory is then quantized using the Dirac’s procedure again, under different gauge-fixing conditions.

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