Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries

TL;DR

This paper develops a collective field theory for a multispecies Calogero model without three-body interactions, revealing duality symmetries that interchange particles and antiparticles, and analyzes ground state properties and fluctuations.

Contribution

It introduces a duality-invariant collective field formulation of the multispecies Calogero model and explores its symmetry group and physical implications.

Findings

Identified duality symmetries forming an Abelian group

Analyzed ground state and small fluctuations for two and multiple species

Extended duality concepts to multispecies Calogero models

Abstract

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.