A classification of generalized quantum statistics associated with classical Lie algebras

Abstract

Articles you may be interested inClassification of generalized quantum statistics associated with the exceptional Lie (super)algebras Statistical quantum probabilities in coherent bosonic and fermionic states A classification of generalized quantum statistics associated with basic classical Lie superalgebras 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 B n =so͑2n +1͒. In this paper, we give a quite general mathematical 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 statistics͒ 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 A n , B n , C n , and D n . In the classification, several new classes of generalized quantum statistics are described.

A classification of generalized quantum statistics associated with basic classical Lie superalgebras

“…Similar triple relations hold for the para-Fermi operators F ξ i [1], see (1.1) in [2]. Both for para-Bose and para-Fermi statistics, there is a group theoretical setting.…”

“…Whether alternative types of generalized quantum statistics can be found in the framework of other classes of simple Lie algebras or superalgebras has been considered in particular by Palev [7]- [15]. Building upon his examples and inspired by the definition of creation and annihilation operators in [11], a mathematical definition of "generalized quantum statistics" was given in [2]. Furthermore, a complete classification was given of all the classes of generalized quantum statistics for the classical Lie algebras A n , B n , C n and D n [2], by means of their algebraic relations.…”

“…Building upon his examples and inspired by the definition of creation and annihilation operators in [11], a mathematical definition of "generalized quantum statistics" was given in [2]. Furthermore, a complete classification was given of all the classes of generalized quantum statistics for the classical Lie algebras A n , B n , C n and D n [2], by means of their algebraic relations. In the present paper we make a similar classification for the basic classical Lie superalgebras.…”

Electromagnetic Excitations of Hall Systems on Four-Dimensional Space

“…This leads to a dressing transformation (51), see also (68), (69), which converts the modified twoform in its undeformed form. The effects of the fluctuations become encoded in the Hamiltonian of the system (70).…”

Algebraic generalization of quantum statistics

“…Therefore para-statistics is associated with representations of the Lie (super)algebras of class B. Motivated by these relations we introduce the concept of a generalized quantum statistics for a classical Lie algebra and classify all the classes of such statistics by means of their algebraic relations [6].…”