We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.

arXiv:hep-th/9503236Modern Physics Letters AMar 28, 19967 citations

PARABOSE-PARAFERMI SUPERSYMMETRY

ALI MOSTAFAZADEH

The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.

arXiv:hep-th/9508106International Journal of Modern Physics AJun 30, 19969 citations

FORMULATION OF QUANTUM STATISTICS

Raj K. Pathria

Elsevier eBooksJan 1, 19720 citations

Lie Algebraical Aspects of the Quantum Statistics. Unitary Quantization (A-quantization)

T. D. Palev

This manuscript was published as a JINR Preprint E17-10550 in 1977. In view of the recent interest in various new kinds of statistics it seems the results it contains may be still of some interest. It is shown that the second quantization axioms can, in principle, be satisfied with creation and annihilation operators generating (in the case of $n$ pairs of such operators) the Lie algebra $A_n$ of the group $SL(n+1)$ . A concept of a Fock space is introduced. The matrix elements of these operators are found.This manuscript was published as a JINR Preprint E17-10550 in 1977. In view of the recent interest in various new kinds of statistics it seems the results it contains may be still of some interest. It is shown that the second quantization axioms can, in principle, be satisfied with creation and annihilation operators generating (in the case of $n$ pairs of such operators) the Lie algebra $A_n$ of the group $SL(n+1)$. A concept of a Fock space is introduced. The matrix elements of these operators are found.

arXiv:hep-th/9705032May 5, 199714 citations

Search for elementary quantum statistics

Carlos A. González-Bernardo, Andrés J. Kálnay

International Journal of Theoretical PhysicsNov 1, 19831 citation

n

pairs of such operators) the Lie algebra

A_n

of the group

SL(n+1)

. A concept of a Fock space is introduced. The matrix elements of these operators are found.