Algebra of Observables for Identical Particles in One Dimension

TL;DR

This paper develops a new algebraic framework for observables of identical particles in one dimension, introducing novel realizations using differentiation operators and matrix models, expanding understanding of particle symmetries.

Contribution

It presents new realizations of the algebra of observables for identical particles, extending previous models with differentiation operators and SU(N)-invariant observables.

Findings

New algebraic realizations in differentiation operators

Introduction of SU(N)-invariant observables in matrix models

Discussion of algebraic structure properties

Abstract

The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here in terms of differentiation operators and in terms of SU(N)-invariant observables of the Hermitian matrix models. Some particular structure properties of the algebra are briefly discussed.