相关论文: Quantum Dynamical Algebra SU(1,1) in One-Dimension…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

We study a class of Calogero-Sutherland type one dimensional N-body quantum mechanical systems, with potentials given by $$ V( x_1, x_2, \cdots x_N) = \sum_{i <j} {g \over {(x_i - x_j)^2}} - \frac{g^{\prime}}{\sum_{i<j}(x_i - x_j)^2} +…

We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…

The problem of equivalency for linear differential operators of the first order is discussed.

We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible…

A symmetry $SU(2,2)$ group in terms of ladder operators is presented for the Jacobi polynomials, $J_{n}^{(\alpha,\beta)}(x)$, and the Wigner $d_j$-matrices where the spins $j=n+(\alpha+\beta)/2$ integer and half-integer are considered…

An exact analytical treatment of the dynamical problem for time-dependent 2x2 pseudo-hermitian su(1,1) Hamiltonians is reported. A class of exactly solvable and physically transparent new scenarios are identified within both classical and…

We study the modular invariance of $N=2$ superconformal $SU(1,1)$ models. By decomposing the characters of Kazama-Suzuki model $SU(3)/(SU(2)\times U(1))$ into an infinite sum of the characters of $(SU(1,1)/U(1))\times U(1)$ we construct…

Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…

We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…

We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…

A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated…

We show that the N=2 superextended 1D quantum Dirac delta potential problem is characterized by the hidden nonlinear $su(2|2)$ superunitary symmetry. The unexpected feature of this simple supersymmetric system is that it admits three…

The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I…

The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, $OSP(2|1)$, as such a symmetry. A number of exactly…

We consider N=1 superpotentials corresponding to gaugings of an underlying extended supergravity for a chiral multiplet in the SU(1,1)/U(1) manifold of curvature 2/3. We analyze the resulting D=4 scalar potentials, and show that they can…

A difference operator realization of quantum deformed oscillator algebra $H_q(1)$ with a Casimir operator freedom is introduced. We show that this $H_q(1)$ have a nonlinear mapping to the deformed quantum su(2) which was introduced by…

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…

It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…