Quantization as a dimensional reduction phenomenon

Details Quantization as a dimensional reduction phenomenon Quantization as a dimensional reduction phenomenon

2006-01-31

arxiv.org/abs/quant-ph/0601209v1

AIP Conf.Proc. 844 (2006) 158-176

Physics

Quantum Physics

19 pages, Talk given by EG at the conference "On the Present Status of Quantum Mechanics", Mali Losinj, Croatia, September 200

Scientific paper

10.1063/1.2219360

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.

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