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Title: A calculus based on a q-deformed Heisenberg algebra

Abstract

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on this derivative differential forms and an exterior differential calculus can be constructed.

Authors:
 [1];  [1];  [2];  [1]
  1. Ludwig Maximilian Univ., Munich (Germany). Sektion Physik; Max Planck Institut fur Physik, Munich (Germany). Werner-Heisenberg-Inst.
  2. Max Planck Institut fur Physik, Munich (Germany). Werner-Heisenberg-Inst.; Univ. Paris-Sud, Orsay (France). Lab. de Physique Theorique et Hautes Energies
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1410300
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
European Physical Journal. C, Particles and Fields
Additional Journal Information:
Journal Volume: 8; Journal Issue: 3; Journal ID: ISSN 1434-6044
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Cerchiai, B. L., Hinterding, R., Madore, J., and Wess, J. A calculus based on a q-deformed Heisenberg algebra. United States: N. p., 1999. Web. doi:10.1007/s100529901097.
Cerchiai, B. L., Hinterding, R., Madore, J., & Wess, J. A calculus based on a q-deformed Heisenberg algebra. United States. doi:10.1007/s100529901097.
Cerchiai, B. L., Hinterding, R., Madore, J., and Wess, J. Tue . "A calculus based on a q-deformed Heisenberg algebra". United States. doi:10.1007/s100529901097. https://www.osti.gov/servlets/purl/1410300.
@article{osti_1410300,
title = {A calculus based on a q-deformed Heisenberg algebra},
author = {Cerchiai, B. L. and Hinterding, R. and Madore, J. and Wess, J.},
abstractNote = {We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on this derivative differential forms and an exterior differential calculus can be constructed.},
doi = {10.1007/s100529901097},
journal = {European Physical Journal. C, Particles and Fields},
number = 3,
volume = 8,
place = {United States},
year = {1999},
month = {4}
}

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