$q$-graded Heisenberg algebras and deformed supersymmetries

Details $q$-graded Heisenberg algebras and deformed supersymmetries $q$-graded Heisenberg algebras and deformed supersymmetries

2009-08-11

arxiv.org/abs/0908.1499v1

Physics

Mathematical Physics

2 figures

Scientific paper

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 disc. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary $\mathbb{Z}_2$ 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 $q\to -1$ for which the Arik and Coon deformation of the Heisenberg algebra allows to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.

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