Bose description of the generalized Pauli spin operators and para super symmetry

In this paper, the generalized fermion algebra is introduced so as to have the [Formula: see text]-dimensional Fock space. The generalized Pauli spin matrices of order [Formula: see text] are introduced by identifying these matrices with the step operators of the generalized fermion algebra. From the [Formula: see text]-graded parity relation [Formula: see text] generalized Pauli matrices are obtained. Finally, the para super symmetry (SUSY) is realized in terms of these matrices and ordinary bosonic operators.

q-Deformed Tamm–Dancoff oscillators: Representation, fermionic extension and physical application

In this paper, the [Formula: see text]-deformed bosonic Tamm–Dancoff oscillator algebra is considered. First, the quantum algebraic and representative properties of these deformed bosons are analyzed in detail. The representations of the [Formula: see text]-fermion algebra of Tamm–Dancoff type are also studied. Second, the high-temperature thermostatistical properties of a gas of Tamm–Dancoff type [Formula: see text]-fermions are investigated. The fermionic distribution function and the other important thermodynamic functions such as the entropy and the specific heat are derived in terms of the real deformation parameter [Formula: see text]. Finally, the time evaluation of a two-level atom in a Tamm–Dancoff oscillator trap interacting with a single-mode traveling light field is concisely discussed.

Generalized fermion algebra

A one-parameter generalized fermion algebra ℬκ(1) is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A special attention is devoted to the limiting case κ → 0, where the fermionic coherent states, labeled by Grassmann variables, are obtained. The physical relevance of the algebra is illustrated throughout Calogero–Sutherland system.

ON THE REPRESENTATION OF THE WIGNER ALGEBRA AND WIGNER DEFORMATION OF THE FERMION ALGEBRA

In this paper, we investigate the representation of the Wigner algebra by using the q-calculus like approach. For this algebra, the coherent state is constructed and the uncertainty relation for the ground state is discussed. Following Wigner's approach, the Wigner deformation of the fermion algebra is obtained and its Fock space is shown to have finite dimension.