SU(2), Associated Laguerre Polynomials and Rigged Hilbert Spaces

TL;DR

This paper explores a new family of SU(2) representations using Laguerre polynomials, connecting them to square-integrable functions on the plane and employing rigged Hilbert spaces for a comprehensive analysis.

Contribution

It introduces a novel realization of SU(2) representations in the plane with Laguerre polynomials and extends the framework using rigged Hilbert spaces.

Findings

Established a connection between Laguerre polynomial-based representations and L^2(R^2) functions.

Demonstrated the use of rigged Hilbert spaces to handle discrete and continuous bases.

Provided insights into the structure of SU(2) representations in the plane.

Abstract

We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere. Relations with an space of square integrable functions defined on the plane, $L^2(\R^2)$, are analyzed. We have also enlarged this study using rigged Hilbert spaces that allow to work with iscrete and continuous bases like is the case here.