2005/10/31 by Nobuhiro Yonezawa, Izumi Tsutsui · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th
paper · pdf · doi:10.1063/1.2162821
published as J.Math.Phys. 47 (2006) 012104 · 24 pages, LaTeX
arxiv created 2005/11/09 · openalex publication_date 2006/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the inequivalent quantizations of the N=3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the “mirror-S3” invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a two-parameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the S3 group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the S3 are universal (parameter-independent) in the family, whereas those corresponding to the doublets of the S3 are dependent on one of the parameters. These properties are shown to be a consequence of the spectral preserving SU(2) (or its subgroup U(1)) transformations allowed in the family of inequivalent quantizations.