Calogero-like Model without Rearrangement Symmetry

0582660 - ÚJF 2025 RIV CH eng J - Journal Article
Znojil, Miloslav
Calogero-like Model without Rearrangement Symmetry.
Symmetry-Basel. Roč. 16, č. 1 (2024), č. článku 27. E-ISSN 2073-8994
Institutional support: RVO:61389005
Keywords : Calogero's A(N) modela * symmetric two-particle barriers * exact solvability requirement * coloring of the Weyl chambers
OECD category: Pure mathematics
Impact factor: 2.7, year: 2022
Method of publishing: Open access
https://doi.org/10.3390/sym16010027

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 - circle plus 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 RA-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.
Permanent Link: https://hdl.handle.net/11104/0350735