The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obta...The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obtain thecanonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any needto introduce unphysical auxiliary fields. As an example we quantize the O(2) nonlinear sigma model using two differentapproaches: the functional Schrodinger method to obtain the wave functionals for the ground and the exited state andthen we quantize the same model using the canonical path integral quantization as an integration over the canonicalphase-space coordinates.展开更多
文摘The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obtain thecanonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any needto introduce unphysical auxiliary fields. As an example we quantize the O(2) nonlinear sigma model using two differentapproaches: the functional Schrodinger method to obtain the wave functionals for the ground and the exited state andthen we quantize the same model using the canonical path integral quantization as an integration over the canonicalphase-space coordinates.
