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arXiv:hep-th/9409163 · Europhysics Letters (EPL)

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

Stjepan Meljanac, Marijan Mileković, Ante Perica

Published Oct 10, 1994• 8 citations
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Abstract

The deformed algebra ( ), 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.

DOI
10.1209/0295-5075/28/2/001

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The deformed algebra ( ), 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.
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Spin-Boson Mappings in the Formalism of fff-Deformations
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Recently, an algebraic generalization of the Jordan-Wigner transformation was introduced and applied to one- and two-dimensional systems. This transformation is composed of the interactions ηi that appear in the Hamiltonian H as H=∑i=1NJiηi, where Ji are coupling constants. In this short note, it is derived that operators that are composed of ηi, or its n-state clock generalizations, satisfy the Dolan-Grady condition and hence obey the Onsager algebra which was introduced in the original solution of the rectangular Ising model and appears in some integrable models.
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