相关论文: SU(N) Coherent States
A basic introduction to the $su(1,1)$ algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of…
We have constructed the quasi-exactly-solvable two-mode bosonic realizations of su(2) and su(1, 1) algebra. We derive the relations leading to the conditions for quasi-exact solvability of two-boson Hamiltonians by determining a general…
We discuss how SU$(1,1)$ coherent states from the discrete series allow for a natural coarse graining operation. The physical application are quantum theories based on a set of three extensive observables whose Poisson algebra is isomorphic…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
Robertson intelligent states which minimize the Schr\" odinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the $su(3)$ algebra. The construction is based on the analytic…
We demonstrate a formally exact quantum-classical correspondence between the stationary coherent states associated with the commensurate anisotropic two-dimensional harmonic oscillator and the classical Lissajous orbits. Our derivation…
Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillator. This allows us to construct the corresponding coherent state in…
It was studied coherent states in complex variables in SU(2), SU(3), SU(4) groups and in general in SU(n) group. Using the completeness relation of the coherent state, we obtain a path integral expression for transition amplitude which…
In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the SU(2,1) group and the deformation quantization of the coset space $D=SU(2,1)/U(2)$ with the method of coherent state…
The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…
We consider the harmonic superspaces associated to SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] ``elementary'' ultrashort analytic superfields…
We study the Dunkl oscillator in two dimensions by the $su(1,1)$ algebraic method. We apply the Schr\"odinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the $su(1,1)$ Lie algebra generators. The energy spectrum…
In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coher- ent states. The suQ(1;1) algebra as a nonlinear deformed algebra realization…
Concerning the new boson representation presented in Part I, it is proved that this representation obeys the su(2)-algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the…
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are…
We exploit SU(N) Schwinger bosons to construct and analyze the coupled irreducible representations of $SU(N) \times SU(N)$ in terms of the invariant group. The corresponding projection operators are constructed in terms of the invariant…
We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete…
An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N=2 supersymmetric SU(n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach…
We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to…
The generalized coherent states for quantum groups introduced by Jurco and Stovicek are studied for the simplest example SU_q(2) in full detail. It is shown that the normalized SU_q(2) coherent states enjoy the property of completeness, and…