A deformed Calogero model accommodates unitary principal series states of sl(2,R) via operator domain changes, preserving unitarity and invariance while altering integrability, with solutions for N=2 and 3.
On the geometry of conformal mechanics
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abstract
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the singularity related to the phenomenon of "falling on the center" is spurious. This opens new possibilities concerning both the interpretation and quantization of the model. Moreover, similar modification seem to be relevant in supersymmetric and multidimensional generalization of conformal mechanics.
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Medicine show: A Calogero model with principal series states
A deformed Calogero model accommodates unitary principal series states of sl(2,R) via operator domain changes, preserving unitarity and invariance while altering integrability, with solutions for N=2 and 3.