0 A ug 1 99 8 C λ - extended oscillator algebra and parasupersymmetric quantum mechanics ∗
نویسندگان
چکیده
C λ-extended oscillator algebra and parasupersymmetric quantum mechanics Abstract The C λ-extended oscillator algebra is generated by {1, a, a † , N, T }, where T is the generator of the cyclic group C λ of order λ. It can be realized as a generalized deformed oscillator algebra (GDOA). Its unirreps can thus be easily exhibited using the representation theory of GDOAs and their carrier space show a Z λ-grading structure. Within its infinite-dimensional Fock space representation, this algebra provides a bosonization of parasupersymmetric quantum mechanics of order p = λ − 1.
منابع مشابه
Cλ-Extended Oscillator Algebras: Theory and Applications to (Variants of) Supersymmetric Quantum Mechanics
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:...
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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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C λ-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra , where C λ is the cyclic group of order λ, have recently proved very useful in the context of supersymmetric quantum mechanics and some of its variants. Here we determine the spectrum generating algebra of the C λ-extended oscillator. We then construct its coherent states, study their nonclassical properties, and comp...
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