A calculus based on a q-deformed Heisenberg algebra

Journal Article · Tue Apr 27 00:00:00 EDT 1999 · European Physical Journal. C, Particles and Fields

DOI:https://doi.org/10.1007/s100529901097· OSTI ID:1410300

Cerchiai, B. L. ^[1]; Hinterding, R. ^[1]; Madore, J. ^[2]; Wess, J. ^[1]

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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

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1410300
• Journal Information: European Physical Journal. C, Particles and Fields, Vol. 8, Issue 3; ISSN 1434-6044
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS