Related papers: Generalized fermion algebra
This paper concerns the construction of $su(r+1)$ Barut--Girardello coherent states in term of generalized Grassmann variables. We first introduce a generalized Weyl-Heisenberg algebra ${\cal A}(r)$ ($r \geq 1$) generated by $r$ pairs of…
We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both…
We describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented.
In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional fermion algebra, and we investigate the properties of this category. The categorical…
We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock…
Parafermionic conformal field theories are considered on a purely algebraic basis. The generalized Jacobi type identity is presented. Systems of free fermions coupled to each other by nontrivial parafermionic type relations are studied in…
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q…
The generalization of $A_r$ statistics, including bosonic and fermionic sectors, is performed by means of the so-called Jacobson generators. The corresponding Fock spaces are constructed. The Bargmann representations are also considered.…
A generalized definition of a deformation of the fermionic oscillator (k-fermionic oscillators) is proposed. Two prescriptions for the construction of generalized Grassmann coherent states for this kind of oscillators are derived. The two…
A $r$-parameter ${u}_{\{\kappa_1, \kappa_2, \cdots, \kappa_r\}}(2)$ algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl-Heisenberg…
Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ${\cal O}_2$ (or ${\cal O}_{2d}$ more generally) are presented by using recursive constructions. As a typical example, an embedding of…
The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral…
In this paper we describe a new family of algebras which in the case of n = 2 reduces to the Fermion algebra and in the limiting case of n tends to infinity reduces to the Boson algebra. These generalized algebras describe particles which…
The aim of this article is to construct \`a la Perelomov and \`a la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This generalized Weyl-Heisenberg algebra, noted A(x), depends on r real parameters and is an…
Notions of a Gaussian state and a Gaussian linear map are generalized to the case of anticommuting (Grassmann) variables. Conditions under which a Gaussian map is trace preserving and (or) completely positive are formulated. For any…
Schr\" odinger-Robertson uncertainty relation is minimized for the quadrature components of Weyl generators of the algebra $su(N)$. This is done by determining explicit Fock-Bargamann representation of the $su(N)$ coherent states and the…
On the basis of the formalism proposed by three of the present authors (A.K., J.P.and M.Y.), generalized Lipkin model consisting of (M+1) single-particle levels is investigated. This model is essentially a kind of the su(M+1)-algebraic…
A unified view of general multimode oscillator algebras with Fock-like representations is presented.It extends a previous analysis of the single-mode oscillator algebras.The expansion of the $a_ia_j^{\dagger}$ operators is extended to…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra ${\cal…