Hamilton--Jacobi quantization of systems with time-dependent constraints (Q1604942)

The paper investigates the quantization of systems with time-dependent constraints by using the Hamilton-Jacobi method. The starting point is the singular Lagrangian of the Hessian matrix introduced by one of the authors [\textit{Y. Güler}, ``Integration of singular systems'', Nuovo Cimento B (11), 1143-1149 (1992)]. The equations of motion are total differential equations in several variables, which lead to a lower dimensional phase space. It is observed that the generalization of Dirac's canonical quantization method in the time-dependent formalism due to \textit{S. P. Gavrilov} and \textit{D. M. Gitman} [Classical Quantum Gravity 10, 57-67 (1993; Zbl 0766.58062)] naturally arises in the Hamilton-Jacobi formalism. The example of a relativistic particle in a plane wave is presented.