Deformed Algebras from Inverse Schwinger Method

TL;DR

This paper introduces an inverse approach to Schwinger's Lie algebra realization, proposing a deformation procedure that reproduces q-deformed and undeformed algebras, with illustrative examples and potential extensions.

Contribution

It presents a novel inverse method for deforming Lie algebras based on Schwinger's construction, expanding the toolkit for algebraic deformations.

Findings

Reproduces q-deformed algebras from undeformed ones

Extends Schwinger's su(1,1) construction to new algebraic forms

Suggests possible extensions of the deformation method

Abstract

We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending Schwinger's $su(1,1)$ construction. As results, various q-deformed algebras are (re-)produced as well as their undeformed counterparts. Some extensions of the method are pointed out briefly.