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.     

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.     

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.     

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 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     

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.     

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 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.     

Supercoherent State and Inhomogeneous Differential Realization of OSP(2, 1) Superalgebra

The supercoherent state of OSP(2, 1) superalgebra is constructed and its propertiesare discussed in detail. The matrix elements of the OSP(2, 1) generators inthe supercoherent state space are calculated. New inhomogeneous differentialrealizations of OSP(2, 1) superalgebra are given.     

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.