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arXiv:hep-th/9604024

Fock Spaces with Reflection Condition and Generalized Statistics

Liu Zhao

Published Apr 4, 1996• 1 citation
arXivHTMLPDF

Abstract

An oscillator algebra and the associated Fock space with reflecting boundary and generalized statistics are constructed and is generalized to the multicomponent case. The oscillator algebra depends manifestly on the reflection factor and the statistical (exchange) factor, and the corresponding Fock space can be obtained from that of the usual bosonic oscillator without reflection condition by certain projection operation.

DOI
10.48550/arxiv.hep-th/9604024

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An oscillator algebra and the associated Fock space with reflecting boundary and generalized statistics are constructed and is generalized to the multicomponent case. The oscillator algebra depends manifestly on the reflection factor and the statistical (exchange) factor, and the corresponding Fock space can be obtained from that of the usual bosonic oscillator without reflection condition by certain projection operation.
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Reflection Equation Algebra of a (h,w)(h,w)(h,w)-deformed Oscillator
We consider the reflection equation algebra for a finite dimensional R-matrix for the (h,w)(h,w)(h,w)-deformed Heisenberg algebra Uh,w(h(4)){\cal U}_{h,w}(h(4))Uh,w​(h(4)). A representation of the reflection matrix KKK is constructed using the matrix generators L(±)L^{(\pm)}L(±) of the Uh,w(h(4)){\cal U}_{h,w}(h(4))Uh,w​(h(4)) algebra. A series of representations of the K-matrix then may be generated by using the coproduct rules of the Uh,w(h(4)){\cal U}_{h,w}(h(4))Uh,w​(h(4)) algebra. The complementary condition necessary for combining two distinct solutions of the reflection equation algebra yields the braiding relations between these two sets of generators. This may be thought as a generalization of Bose-Fermi statistics to braiding statistics, which them may be used to provide a new braided colagebraic structure to a Hopf algebra generated by the elements of the matrix KKK. The reflection equation algebra and the braided exchange properties are found to depend on both deformation parameters hhh and www.