On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system

TL;DR

This paper derives the spectra of action-variables in the quantized compactified Ruijsenaars-Schneider system using Kahler quantization and classical-quantum correspondence, confirming previous Schrödinger quantization results.

Contribution

It provides a simple derivation of the spectra by combining Kahler quantization with classical action-variables as a toric moment map.

Findings

Spectra obtained via Kahler quantization match previous Schrödinger quantization results.

Classical action-variables identified as a toric moment map on complex projective space.

Method offers a straightforward approach to quantization of the system.

Abstract

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.