Cλ-Extended Oscillator Algebras: Theory and Applications to (Variants of) Supersymmetric Quantum Mechanics
نویسنده
چکیده
Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof: an algebraic realization of supersymmetric quantum mechanics for cyclic shape invariant potentials of period λ, a bosonization of parasupersymmetric quantum mechanics of order p = λ − 1, and, for λ = 3, a bosonization of pseudosupersymmetric quantum mechanics and orthosupersymmetric quantum mechanics of order two.
منابع مشابه
Cλ-extended oscillator algebras and some of their deformations and applications to quantum mechanics
Cλ-extended oscillator algebras generalizing the Calogero-Vasiliev algebra, where Cλ is the cyclic group of order λ, are studied both from mathematical and applied viewpoints. Casimir operators of the algebras are obtained, and used to provide a complete classification of their unitary irreducible representations under the assumption that the number operator spectrum is nondegenerate. Deformed ...
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