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AIP Conf. Proc. / Volume 844 / Issue 1

Quantization as a dimensional reduction phenomenon

AIP Conf. Proc. -- June 27, 2006 -- Volume 844, pp. 158-176
QUANTUM MECHANICS: Are There Quantum Jumps? - and On the Present Status of Quantum Mechanics; doi:10.1063/1.2219360

Issue Date: 27 June 2006

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ABSTRACT

CITING ARTICLES

E. Gozzi and D. Mauro
Department of Theoretical Physics, University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste, Italy
INFN, Sezione di Trieste, Italy

Classicalmechanics, in the operatorial formulation of Koopman and von Neumann,can be written also in a functional form. In thisform two Grassmann partners of time make their natural appearanceextending in this manner time to a three dimensional supermanifold.Quantization is then achieved by a process of dimensional reductionof this supermanifold. We prove that this procedure is equivalentto the well-known method of geometric quantization. ©2006 American Instituteof Physics

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