Coherent State and Inhomogeneous Differential Realization of the SPL(2,1) Superalgebra

The simple coherent state of the SPL(2,1) superalgebra is constructed and its properties are discussed in detail. The matrix elements of the SPL(2,1) generators in the coherent state space are calculated. A new form for the homogeneous differential realization of the SPL(2,1) superalgebra is given.     

SPL(2,1)超代数的齐次和非齐次微分实现及其玻色-费密实现

研究了特殊线性李超代数SPL(2,1)在齐次和非齐次多项式空间上的微分实现,以及对应的齐次和非齐次玻色-费密实现。     

One-Parameter Indecomposable Representation of SPL(2,1) Superalgebra

Using inhomogeneous boson–fermion realization one-parameter indecomposable representation of the SPL(2,1) superalgebra is studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg-Weyl superalgebra. PACS: 12.60.Jv; 03.65.FdThe author was supported financially by Shenzhen Institute of Information Technology.     

One-Parameter Inhomogeneous Differential Realization and Boson-Fermion Realization of the SPL(2,1) Superalgebra

One-parameter inhomogeneous differential realization of the SPL(2,1) superalgebra on the space of homogeneous polynomials and the corresponding boson-fermion realization are studied. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons.     

One-Parameter Homogeneous Differential Realization and Boson–Fermion Realization of the SPL(2,1) Superalgebra

One-parameter homogeneous differential realization of the SPL(2,1) superalgebra on the space of homogeneous polynomials and the corresponding boson–fermion realization are studied. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons.The author was supported financially by Shenzhen Institute of Information Technology grant No. LG-060109. PACS: 12.60.Jv, 03.65.FD     

Simple Coherent State and New Form for Inhomogeneous Differential Realization of OSP(2,1) Superalgebra

The simple coherent state of the OSP(2,1) superalgebra is constructed and its properties are discussed in detail. The matrix elements of the OSP(2,1) generators in the coherent state space are calculated. The new form for inhomogeneous differential realization of the OSP(2,1) superalgebra is given.     

Supercoherent-state representation of the OSP(2,1) superalgebra

The supercoherent state of the OSP(2,1) superalgebra is constructed and its properties are discussed in detail. An inhomogeneous differential realization of the OSP(2,1) superalgebra on the supercoherent-state space is given. It may be of use for determining new concrete structure of the quasi-exactly-solvable Hamiltonian corresponding to the OSP(2,1) supersymmetric quantum system.     

On One-Parameter Supercoherent State Representation of the gl(2,1) Superalgebra

One-parameter supercoherent state of the gl(2,1) superalgebra is constructed. Its properties are discussed in detail. An arbitrary vector can be expanded in terms of the supercoherent state for the gl(2,1) superalgebra.     

One-Parameter General Coherent State of the gl(2,1) Superalgebra

One-parameter general coherent state of the gl(2,1) superalgebra is constructed. Its properties are discussed in detail. One-parameter matrix elements of the gl(2,1) generators in the one-parameter general coherent-state space are calculated.     

SPL(2，1)超代数的不可分解表示和不可约表示

利用ＳＰＬ（２,１）的非齐次玻色 费米实现,研究了ＳＰＬ（２,１）在Ｈｅｉｓｅｎｂｅｒｇ Ｗｅｙｌ超代数的广义包络代数的子空间和商空间上的不可分解表示和不可约表示,并给出了它的全部有限维不可约表示 关键词：     

One-Parameter Coherent State Representation of the spl(2,1) Superalgebra

One-parameter general coherent states of the spl(2,1) superalgebra are constructed and their properties are discussed in detail. One-parameter matrix elements of the spl(2,1) generators in the one-parameter general coherent-state space are calculated. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons.     

Differential Operator Realization of the Exceptional Superalgebra D(2,1;α) and Its Application

In this paper, we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α). Based on these expressions, we construct free field realizations of the currents associated with D(2,1;α) at an arbitrary level k.     

One-Parameter Irreducible Representation of spl(2,1) Superalgebra

One-parameter irreducible representation of the spl(2,1) superalgebra is studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg-Weyl superalgebra. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons. The author was supported financially by Shenzhen science and technology plan project and Shenzhen Institute of Information Technology Grant No. szkj0711.     

On One-Parameter Supercoherent State of spl(2,1) Superalgebra

One-Parameter supercoherent state of the spl(2,1) superalgebra is constructed and its properties are discussed in detail. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons. The author was supported financially by Shenzhen science and technology plan project and Shenzhen Institute of Information Technology Grant No. szkj0711.     

Two-parameter extended Hubbard Hamiltonian with supersymmetry

We investigate under which circumstances extended Hubbard models, including bond-charge, exchange, and pair-hopping terms, are invariant under gl (2,1) superalgebra. This happens for a two-parameter Hamiltonian which includes as particular cases the t - J, the EKS and the one-parameter BGLZ Hamiltonians, all integrable in one dimension. We show that the two parameter Hamiltonian can be recasted as the sum of the BGLZ Hamiltonian plus the graded permutation operator of electronic states on neighbouring sites. The integrability of the corresponding one-dimensional model is discussed. Received: 17 February 1998 / Received in final form: 6 March 1998 / Accepted: 17 April 1998     

U(1/1)q q-Coherent States and Path Integrals for the q-Deformed Jaynes-Cummings Model

The q-coherent states for the quantum superalgebra U(1/1)_q, are introduced. Path integrals in the q-coherent state representations of the U(1/1)_q, are constructed and applied to the q-deformed Jaynes-Cummings model whose dynamical superalgebra is the quantum superalgebra U(1/1)_q.     

INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS

The differential realization of Lie superalgebra B(0,1) on the space of inhomogeneous polynomials,and the corresponding inhomogeneous Boson-Fermion realization are studiel.A new kind of indecomposable and irreducible representations of Lie superalgebra B(0,1) is studied on the universal enveloping algebra of Heisenberg-Weyl superalgebra,and on its subspaces and quotient spaces.All the finite dimensional irreducible representations are naturally obtained as special cases.     

sh(2/2) Superalgebra Eigenstates and Generalized Supercoherent and Supersqueezed States

The superalgebra eigenstates (SAES) concept is introduced and then applied to find SAES associated to the sh(2/2) superalgebra, also known as Heisenberg–Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2)Ð sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg–Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the super-Hermitian and -pseudo-super-Hermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.     

One-Parameter Indecomposable and Irreducible Representations of gl(2 | 1) Superalgebra

Using inhomogeneous boson–fermion realization, one-parameter indecomposable and irreducible representations of the gl(2 | 1) superalgebra are studied on subspace and quotient spaces of the universal enveloping algebra of Heisenberg–weyl superalgebra. All the finite-dimensional irreducible representations of one-parameter of the gl(2 | 1) superalgebra are naturally obtained as special cases. The parameter has relation to the Hubbard interaction parameter U in the Hubbard model for correlated electrons.     

On Two-Parameter Deformations of osp(1|2)(1)

An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra osp(1|2)⁽¹⁾ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of infinite Hopf family of superalgebras, a generalization of the infinite Hopf family of algebras proposed earlier by the authors. The trigonometric and rational degenerations are briefly discussed.