Quantization is geometry, after all
type: Item
instance of: scholarly article
title: Quantization is geometry, after all
zbMATH Open document ID: 0648.53052
DOI: 10.1016/0003-4916(88)90092-9
author: J. R. Klauder
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: Quantization of a general canonically formulated classical theory is expressed in a geometric fashion utilizing the symplectic structure of phase space augmented by one of several acceptable Riemannian metric structures appended to the phase-space manifold. The purpose of the metric is to provide an adequate geometrical structure on phase space to support Brownian motion which is used in a path-integral-like quantization procedure. For a wide class of Hamiltonian the propagator of the quantum theory is given a rigorous, unambiguous, and completely geometric interpretation that is covariant under arbitrary canonical coordinate transformations. In this procedure different appended Riemannian geometries result in a quantization involving completely inequivalent sets of quantum kinematical variables. In particular, for Heisenberg variables this quantization procedure provides a natural geometric explanation of why the usual Schrödinger representation applies to only a very limited set of canonical coordinates and not to all such coordinates.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 81S40
zbMATH DE Number: 4058371
zbMATH Keywords: symplectic structure
zbMATH Keywords: phase space
zbMATH Keywords: Brownian motion
zbMATH Keywords: path-integral-like quantization procedure
zbMATH Keywords: appended Riemannian geometries
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90092-9
OpenAlex ID: W1972397224
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description: scientific article; zbMATH DE number 4058371