A classification of generalized quantum statistics associated with classical Lie algebras

Generalized quantum statistics such as para-Fermi statistics is characterized by certain triple relations which, in the case of para-Fermi statistics, are related to the orthogonal Lie algebra Bn = so(2n + 1). In this paper, we give a quite general definition of “a generalized quantum statistics associated to a classical Lie algebra G”. This definition is closely related to a certain Z-grading of G. The generalized quantum statistics is then determined by a set of root vectors (the creation and annihilation operators of the statistics) and the set of algebraic relations for these operators. Then we give a complete classification of all generalized quantum statistics associated to the classical Lie algebras An, Bn, Cn and Dn. In the classification, several new classes of generalized quantum statistics are described. Running title: Classification of generalized statistics PACS: 02.20.+b, 03.65.Fd, 05.30-d. Permanent address: Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria