Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

Fring, A. & Korff, C. (2004). Exactly solvable potentials of Calogero type for q-deformed Coxeter groups. Journal of Physics A: Mathematical and General, 37(45), pp. 10931-10949. doi: 10.1088/0305-4470/37/45/012

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Abstract

We establish that by parametrizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite-dimensional representation spaces of a Lie algebra. We present explicitly the Gq2-case for which we construct the potentials by means of suitable gauge transformations.

Item Type: Article
Uncontrolled Keywords: MANY-BODY PROBLEM, ONE DIMENSION, MOSER MODELS, LIE-ALGEBRAS, INTEGRABLE SYSTEM, SUTHERLAND MODELS, FIELD-THEORIES, QUANTUM, SOLVABILITY, STATE
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/798

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