All the Exact Solutions of Generalized Calogero-Sutherland Models

TL;DR

This paper extends a collective field method to find all explicit solutions of generalized Calogero-Sutherland models associated with classical groups, including spinor representations, providing a comprehensive solution set.

Contribution

It introduces a method to obtain all explicit solutions for generalized Calogero-Sutherland models linked to classical groups, including spinor cases, which was not previously achieved.

Findings

All explicit solutions for models based on classical groups are obtained.

Solutions include those corresponding to spinor representations for B_N and D_N.

The method provides a complete characterization of solutions for these models.

Abstract

A collective field method is extended to obtain all the explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of all the classical groups, including the solutions corresponding to spinor representations for $B_N$ and $D_N$ cases.