Deformed Heisenberg algebra with reflection
Abstract
A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional representations of the parafermionic nature. We demonstrate that finite-dimensional representations are representations of deformed parafermionic algebra with internal Z_2-grading structure. On the other hand, any finite- or infinite-dimensional representation of the algebra supply us with irreducible representation of osp(1|2) superalgebra. We show that the normalized form of deformed Heisenberg algebra with reflection has the structure of guon algebra related to the generalized statistics.
Cite
@article{arxiv.hep-th/9701091,
title = {Deformed Heisenberg algebra with reflection},
author = {Mikhail Plyushchay},
journal= {arXiv preprint arXiv:hep-th/9701091},
year = {2009}
}
Comments
16 pages, LaTeX, to appear in Nucl. Phys. B