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

Abstract

The deformed algebra $\mathcal{A}(\mathcal{R})$, 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.

10+ii pages,preprint RBI-TH-10/93,Latex,(to appear in Europhys.Lett.)

References in corpus (7)

• The complete solution to the constant quantum Yang-Baxter equation in two dimensions
• Anyons and Quantum Groups
• Bose-Fermi Transformation In Three Dimensional Space
• Unified View of Deformed Single - Mode Oscillator Algebras
• Anyons as quon particles
• Example of q-deformed Field Theory
• A New Deformed Supersymmetric Oscillator

Cited by in corpus (5)

• Exclusion statistics,operator algebras and Fock space representations
• Quantum computation from fermionic anyons on a 1D lattice
• Interpolation between para-Bose and para-Fermi statistics
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• A New Deformed Supersymmetric Oscillator