q-graded Heisenberg algebras and deformed supersymmetries

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3272545· OSTI ID:21335914

Ben Geloun, Joseph ^[1]; Hounkonnou, Mahouton Norbert ^[2]

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1. National Institute for Theoretical Physics (NITheP), Private Bag X1, Matieland 7602 (South Africa)
2. International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), 072 BP 50 Cotonou (Benin)

The notion of q-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for q complex number in the unit disk. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary Z{sub 2} grading or Grassmann parity for associative superalgebra and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit q{yields}-1 for which the Arik and Coon deformation [J. Math. Phys. 17, 524 (1976)] of the Heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.

• OSTI ID: 21335914
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 2; Other Information: DOI: 10.1063/1.3272545; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BY-PRODUCTS
FERMIONS
HARMONIC OSCILLATORS
PARITY
SUPERSYMMETRY