Lie algebraic noncommuting structures from reparametrization symmetry

Journal Article · Tue May 15 04:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2723551· OSTI ID:20929708

Gangopadhyay, Sunandan ^[1]

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1. S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700098 (India)

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrization symmetry. We show explicitly (in contrast to the earlier results in our paper [R. Banerjee et al. J. Phys. A 38, 957 (2005), e-print hep-th/0405178]) that for some special choices of the reparametrization parameter {epsilon}, one can obtain space-space noncommuting structures which are Lie algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of {epsilon} for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.

• OSTI ID: 20929708
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ANGULAR MOMENTUM
COMMUTATION RELATIONS
LIE GROUPS
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SPACE-TIME
SYMMETRY