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

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.

4 pages, 1 ref. updated with respect to the journ. version

References in corpus (2)

• Ladder operators, Fock-spaces, irreducibility and group gradings for the Relative Parabose Set algebra
• Space Structure for the Simplest Parasupersymmetric System

Cited by in corpus (12)

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• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces
• Graded colour Lie superalgebras for solving Lévy-Leblond equations
• On a class of Fock-like representations for Lie Superalgebras
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces
• The parastatistics Fock space and explicit Lie superalgebra representations
• Gradings, Braidings, Representations, Paraparticles: some open problems
• A Klein operator for paraparticles
• Towards applications of graded Paraparticle algebras