R-deformed Heisenberg algebra

Mikhail Plyushchay

doi:10.1142/s0217732396002927

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arXiv · hep-th/9701065

R-deformed Heisenberg algebra

Mikhail Plyushchay

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Abstract

It is shown that the deformed Heisenberg algebra involving the reflection operator R (R-deformed Heisenberg algebra) has finite-dimensional representations which are equivalent to representations of paragrassmann algebra with a special differentiation operator. Guon-like form of the algebra, related to the generalized statistics, is found. Some applications of revealed representations of the R-deformed Heisenberg algebra are discussed in the context of OSp(2|2) supersymmetry. It is shown that these representations can be employed for realizing (2+1)-dimensional supersymmetry. They give also a possibility to construct a universal spinor set of linear differential equations describing either fractional spin fields (anyons) or ordinary integer and half-integer spin fields in 2+1 dimensions.

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Mikhail Plyushchay. 1997-01-14. R-deformed Heisenberg algebra. https://doi.org/10.1142/s0217732396002927

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