Interacting families of Calogero-type particles and SU(1,1) algebra
Abstract
We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1) generators for the whole system are composed of SU(1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.