English

Unique Closed-Form Quantization Via Generalized Path Integrals or by Natural Extension of the Standard Canonical Recipe

High Energy Physics - Theory 2008-02-03 v2 Nuclear Theory Quantum Physics

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