Calogero-like Model without Rearrangement Symmetry.

Reinterpretation of mathematics behind the exactly solvable Calogero's A-particle quantum model is used to propose its generalization. Firstly, it is argued that the strongly singular nature of Calogero's particle–particle interactions makes the original permutation-invariant Hamiltonian tractable as a direct sum H = ⨁ H a of isospectral components, which are mutually independent. Secondly, after the elimination of the center-of-mass motion, the system is reconsidered as existing in the reduced Euclidean space R A − 1 of relative coordinates and decaying into a union of subsets W a called Weyl chambers. The mutual independence of the related reduced forms of operators H a enables us to makes them nonisospectral. This breaks the symmetry and unfolds the spectral degeneracy of H. A new multiparametric generalization of the conventional A-body Calogero model is obtained. Its detailed description is provided up to A = 4 . [ABSTRACT FROM AUTHOR]