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arXiv · 1105.4819

Graded Fock--like representations for a system of algebraically interacting paraparticles

K. Kanakoglou·A. Herrera-Aguilar
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Abstract

We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom $P_{BF}^{(1,1)}$, we will study a class of Fock--like representations of this algebra, dependent on a positive integer parameter p (a kind of generalized parastatistics order). Mathematical properties of the Fock--like modules will be investigated for all values of p and constructions such as ladder operators, irreducibility (for the carrier spaces) and Klein group gradings (for both the carrier spaces and the algebra itself) will be established.

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K. Kanakoglou, A. Herrera-Aguilar. 2011-05-24. Graded Fock--like representations for a system of algebraically interacting paraparticles. https://doi.org/10.1088/1742-6596%2F287%2F1%2F012037

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