On the R-Matrix Formulation of Deformed Algebras and Generalized Jordan-Wigner Transformations

TL;DR

This paper explores the algebraic structure of deformed algebras based on Yang-Baxter R-matrices, identifying conditions for associativity and introducing generalized Jordan-Wigner transformations for multimode oscillators.

Contribution

It extends the boson realization of fermions to multimode oscillators and constructs four solutions satisfying associativity conditions for deformed algebras.

Findings

Four solutions satisfying associativity conditions are constructed.

Two solutions can be represented by generalized Jordan-Wigner transformations.

The work extends boson realization from single-mode to multimode oscillators.

Abstract

The deformed algebra $\cal{A(R)}$, depending upon a Yang-Baxter R- matrix, is considered. The conditions under which the algebra is associative are discussed for a general number of oscillators. Four types of solutions satisfying these conditions are constructed and two of them can be represented by generalized Jordan-Wigner transformations.Our analysis is in some sense an extension of the boson realization of fermions from single-mode to multimode oscillators.