On the Hydrogen Atom via Wigner-Heisenberg Algebra

Cat-States in the Framework of Wigner-Heisenberg Algebra

A one-parameter generalized Wigner-Heisenberg algebra( WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule $[\hat{x}, \hat{p}_λ] = i(1 + 2λ\hat{R})$ and also highlights the dynamical symmetries of the pseudo-harmonic oscillator( PHO). \textbf{The present article is devoted to the study of new cat-states} built from $λ$-deformed Schrödinger coherent states, which according to the Barut-Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states…

Polynomial Heisenberg algebras, multiphoton coherent states and geometric phases

In this paper we will realize the polynomial Heisenberg algebras through the harmonic oscillator. We are going to construct then the Barut-Girardello coherent states, which coincide with the so-called multiphoton coherent states, and we will analyze the corresponding Heisenberg uncertainty relation and Wigner distribution function for some particular cases. We will show that these states are intrinsically quantum and cyclic, with a period being a fraction of the oscillator period. The associated geometric phases will be as well evaluated.

Wigner振子、扭曲Hopf代数与二次量子化

Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

通过正确识别中心扩张在中心扩张Heisenberg代数h中的作用，我们证明了在相应的包络代数U（h）上构造一个Hopf代数结构并最终通过Drinfeld扭曲使其变形是可能的.这种Hopf代数结构及其变形形式U^F（h）是从薛定谔场/振子代数及其变形形式得到的一个更基本的Hopf代数导出的，只要场/振子被视为超代数osp（1）的奇元|2n）。我们还讨论了在量子统计的背景下可能的影响。

非对易平面上任意子的玻色化超对称性和超对称奇异粒子

Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane

利用玻色Heisenberg代数的Wigner变形，提出了一个描述（2+1）D中N=1超对称任意子系统的线性微分场方程的协变组.非相对论性的“Jackiw-Nair”极限从Heisenberg-Wigner代数中提取了普通的玻色子和费米子自由度。它产生一阶，非相对论性波动方程的自旋粒子的非对易平面，承认伽利略异国情调的平面N=1超对称。

离散海森堡群$HW_{2^s}$的酉不可约表示完全集

Complete set of unitary irreps of Discrete Heisenberg Group $HW_{2^s}$

本研究采用Wigner-Mackay诱导群表示方法，构造离散有限海森堡-外尔群$HW_{2^s}$的全部酉不可约表示，确定其特征标与融合规则，为有限量子力学、量子计算提供理论支撑。