Quantization as a dimensional reduction phenomenon
量子物理
2009-11-13 v1 高能物理 - 理论
摘要
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.
引用
@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}
}
备注
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