Unique Closed-Form Quantization Via Generalized Path Integrals or by Natural Extension of the Standard Canonical Recipe
Abstract
Description
The Feynman-Garrod path integral representation for time evolution is extended to arbitrary one-parameter continuous canonical transformations. One thereupon obtains a generalized Kerner-Sutcliffe formula for the unique quantum representation of the transformation generator, which can be an arbitrary classical dynamical variable. This closed-form quantization procedure is shown to be equivalent to a natural extension of the standard canonical quantization recipe -- an extension that resolves the operator-ordering ambiguity in favor of the Born-Jordan rule.
6 pages, LaTeX, Revised to refer to the earlier Kerner-Sutcliffe Hamiltonian quantization formula and to the Born-Jordan operator ordering rule. Also now gives the generalizations to multiple degrees of freedom and continuum fields
6 pages, LaTeX, Revised to refer to the earlier Kerner-Sutcliffe Hamiltonian quantization formula and to the Born-Jordan operator ordering rule. Also now gives the generalizations to multiple degrees of freedom and continuum fields