Hamilton-Jacobi Quantization of General Relativity

Abstract

It is shown that the family of solutions of the Einstein field equations, determined by a solution of the Hamilton-Jacobi equations, is characterized by a complete commuting set of constants of the motion. It is then pointed out that the quantization program based on the utilization of the transition from the Hamilton-Jacobi equations to the corresponding Schrödinger equations yields a quantum thoery of gravitation which is "frozen" (that is, it contains no dynamics), thus suffering from the same malady as does the canonical quantization program.