Year: 2012
Type: preprint
Abstract: In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires noncommutative one (q-numbers). The rest of theory can be unchanged. In this paper we critically review Dirac's proposition. We provide a natural formulation of classical mechanics through noncommutative quantities with a non-zero Planck constant. This is done with the help of the nilpotent unit, which squares to zero. Thus, the crucial rôle in quantum theory shall be attributed to the usage of complex numbers. The paper provides English and Russian versions.
Source: arXiv (Cornell University)
Author: Kisil, Vladimir V.
Institution: University of Leeds
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1574056404