2 research outputs found
Matrix oscillator and Calogero-type models
We study a single matrix oscillator with the quadratic Hamiltonian and
deformed commutation relations. It is equivalent to the multispecies Calogero
model in one dimension, with inverse-square two-body and three-body
interactions. Specially, we have constructed a new matrix realization of the
Calogero model for identical particles, without using exchange operators. The
critical points at which singular behaviour occurs are briefly discussed.Comment: Accepted for publication in Phys.Lett.
Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
We study the collective field formulation of a restricted form of the
multispecies Calogero model, in which the three-body interactions are set to
zero. We show that the resulting collective field theory is invariant under
certain duality transformations, which interchange, among other things,
particles and antiparticles, and thus generalize the well-known strong-weak
coupling duality symmetry of the ordinary Calogero model. We identify all these
dualities, which form an Abelian group, and study their consequences. We also
study the ground state and small fluctuations around it in detail, starting
with the two-species model, and then generalizing to an arbitrary number of
species.Comment: latex, 53 pages, no figures;v2-minor changes (a paragraph added
following eq. (61)