Quantization as a dimensional reduction phenomenon
Quantum Physics
2009-11-13 v1 High Energy Physics - Theory
Abstract
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three dimensional supermanifold. Quantization is then achieved by a process of dimensional reduction of this supermanifold. We prove that this procedure is equivalent to the well-known method of geometric quantization.
Cite
@article{arxiv.quant-ph/0601209,
title = {Quantization as a dimensional reduction phenomenon},
author = {E. Gozzi and D. Mauro},
journal= {arXiv preprint arXiv:quant-ph/0601209},
year = {2009}
}
Comments
19 pages, Talk given by EG at the conference "On the Present Status of Quantum Mechanics", Mali Losinj, Croatia, September 2005. New results are contained in the last part of the paper