Abstract
We review some of the uses of the spectrum generating algebra approach using conventional Lie algebras applied to exactly solvable many-body models. We compare these to the possible applications of spectrum generating q-algebras. We describe a generalized deformation of the canonical commmutation relations (CCR), which reduce both to the CCR for standard q-bosons, and to the Canonical Anti-commutation Relations (CAR) for fermions in appropriate limits. By a choice of the deformation, we show that the new “qummutation relations” define bosonic-type particles having finite number occupancy (anyons) and relate these to standard descriptions of anyons, and use them to construct a model hamiltonian for interacting anyons which has the quantum group SU q (2) as dynamical group.
To Franco Iachello, who has shown us that experiment is the motive force of theory.
Talk contributed to SYMMETRIES IN SCIENCE VII: Spectrmn Generating Algebras and Dynamic Symmetries in Physics, on the occasion of the fiftieth birthday of Professor Franco Iachello.
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Solomon, A.I., Birman, J.L. (1994). Spectrum Generating q-Algebras for Anyons. In: Gruber, B., Otsuka, T. (eds) Symmetries in Science VII. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2956-9_46
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DOI: https://doi.org/10.1007/978-1-4615-2956-9_46
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