Unique Closed-Form Quantization Via Generalized Path Integrals or by Natural Extension of the Standard Canonical Recipe
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9505189,
title = {Unique Closed-Form Quantization Via Generalized Path Integrals or by Natural Extension of the Standard Canonical Recipe},
author = {S. K. Kauffmann},
journal= {arXiv preprint arXiv:hep-th/9505189},
year = {2008}
}
Comments
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