Medicine show: A Calogero model with principal series states
Tarek Anous, Jackson R. Fliss, Jeremy van der Heijden

TL;DR
This paper modifies the Calogero model to include principal series states, preserving unitarity and symmetry but changing integrability, and provides explicit solutions for small particle numbers.
Contribution
It introduces a deformed Calogero model accommodating principal series states, expanding the model's applicability and offering a method for solving it at any particle number.
Findings
Successfully incorporates principal series states into the Calogero model.
Preserves unitarity and $rak{sl}(2,b R)$-invariance despite deformation.
Provides explicit solutions for $N=2,3$ and outlines a general solution procedure.
Abstract
The Calogero model is an interacting, -particle, -invariant quantum mechanics, whose Hilbert space is furnished by a tower of discrete series modules. The system enjoys both classical and quantum integrability at any and at any value of the coupling; this is guaranteed by the existence of mutually-commuting currents, one of them being the Hamiltonian. In this paper, we alter the Calogero model so that it may accommodate states in the unitary principal series irreducible representation of . Doing so requires changing the domain of the quantum operators--a procedure which succeeds in preserving unitarity and -invariance, but alters the integrability properties of the theory. We explicitly solve the deformed model for and outline a procedure for solving the model at general . We expect…
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