Improved Hamilton-Jacobi Quantization for a Nonholonomic System

Abstract

A nonholonomic constrained system with second-class constraints is investigated using the Hamilton-Jacobi quantization (HJ) scheme to yield the complete equations of motion of the system. Although the integrability conditions in the HJ scheme are equivalent to the involutive relations for a first-class constrained system in the improved Dirac quantization method (DQM), one should elaborate the HJ scheme by using the improved DQM in order to obtain the first-class Hamiltonian and the corresponding effective Lagrangian having the Becci-Rouet-Stora-Tyutin invariant nonholonomic constrained system.