The Canonical Path Integral Quantization of CP1 Model

The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion are obtained as total differential equations in many variables. It is shown that if the system is integrable, then one can obtain the canonical phase space coordinates and the set of the canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields. As an example we quantize the CP¹ model using the canonical path integral quantization formalism to obtain the path integral as an integration over the canonical phase-space coordinates.