Title
Minimal length scale in quantum mechanics from a deformation quantization perspective
Authors
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee
Scientific discipline (Law 2.0)
Year of publication
2024
Published in
Article type
scientific article
Publication language
english
Abstract
EN We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.
Pages (from - to)
012044-1 - 012044-8
Comments
Article number: 012044
License type
CC BY (attribution alone)
Open Access Mode
open journal
Open Access Text Version
final published version
Date of Open Access to the publication
at the time of publication
Full text of article
Access level to full text
public
Ministry points / journal
40
System created by Poznań University of Technology
and Poznan Supercomputing and Networking Center
Log in through eKonto to add to SIS