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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

New classification of particles statistics

Leonardo Falco, Roberto Scipioni

Published Sep 1, 1994• 4 citations
Publisher
DOI
10.1007/bf02780712

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A new generalization of quantum statistics is described, which is different from parastatistics, though it includes Fermi statistics and parafermi statistics of order two. It can be applied to the quantization of nonlinear field theories, without violating the correspondence principle. Like parastatistics, it allows the occupation of a given dynamical state by more than one particle of half-odd-integral spin. A special feature is that quark-like particles are naturally associated in modules, which have many of the characteristics of baryons and mesons. The group theoretical properties of the new statistics, and the implied classification of states, are briefly examined.
We consider the compatibility conditions for an N -particle D -dimensional Wigner quantum oscillator. These conditions can be rewritten as certain triple relations involving anticommutators, so it is natural to look for solutions in terms of Lie superalgebras. In the recent classification of 'generalized quantum statistics' for the basic classical Lie superalgebras [1], each such statistics is characterized by a set of creation and annihilation operators plus a set of triple relations. In the present paper, we investigate which cases of this classification also lead to solutions of the compatibility conditions. Our analysis yields some known solutions and several classes of new solutions.
We consider the compatibility conditions for a N-particle D-dimensional Wigner quantum oscillator. These conditions can be rewritten as certain triple relations involving anticommutators, so it is natural to look for solutions in terms of Lie superalgebras. In the recent classification of “generalized quantum statistics ” for the basic classical Lie superalgebras [1], each such statistics is characterized by a set of creation and annihilation operators plus a set of triple relations. In the present letter, we investigate which cases of this classification also lead to solutions of the compatibility conditions. Our analysis yields some known solutions and several classes of new solutions.