Algebraic generalization of quantum statistics
نویسندگان
چکیده
Generalized quantum statistics such as para-Bose and para-Fermi statistics are related to the basic classical Lie superalgebras B(0|n) and Bn. We give a quite general definition of “a generalized quantum statistics associated to a Lie superalgebra G”. This definition is closely related to a certain Z-grading of G. The generalized quantum statistics is 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 Lie superalgebras An, Bn, Cn, Dn, G2, F4, E6, E7, E8, A(m|n), B(m|n), C(n), D(m|n), G(3), F (4) and D(2, 1;α).
منابع مشابه
Lie algebraic generalization of quantum statistics
Para-Fermi statistics and Fermi statistics are known to be associated with particular representations of the Lie algebra so(2n+1)≡ Bn. Similarly paraBose and Bose statistics are related with the Lie superalgebra osp(1|2n)≡ B(0|n). We develop an algebraical framework for the generalization of quantum statistics based on the Lie algebras An, Bn, Cn and Dn.
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