A Klein operator for paraparticles

Abstract

It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of $m$ parafermions and a set of $n$ parabosons. These two choices are known as ``relative parafermion type'' and ``relative paraboson type'', and correspond to quite different underlying algebraic structures. In this short note we show how the two possibilities are related by a so-called Klein transformation.

References in corpus (4)

• Once more on parastatistics
• Graded Fock--like representations for a system of algebraically interacting paraparticles
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces