论文标题
相干状态和广义的Hermite多项式用于分数统计 - 从费米斯到玻色子
Coherent States and Generalized Hermite Polynomials for fractional statistics -- interpolating from fermions to bosons
论文作者
论文摘要
本文开发了代数结构，该代数结构是由$θ$ -Commutator $αβ-e^{Iθ}βα= 1 $ $ $的，该结构提供了Clifford和Heisenberg代数之间的连续插值。我们首先演示了最一般的几何图片，适用于所有$ n $的值。在列出了希尔伯特空间的属性之后，我们研究了广义相干状态，这些状态在$ξ^n = 0 $时，以$ n \ ge 2 $。我们还解决了通用的谐波振荡器问题，并为一般$ n $提供了赫米特多项式的广义版本。有一些评论将这项研究与Anyons的情况联系起来。这项研究代表着发展任何田间理论的第一步。
This article develops the algebraic structure that results from the $θ$-commutator $αβ- e^{i θ} βα= 1 $ that provides a continuous interpolation between the Clifford and Heisenberg algebras. We first demonstrate the most general geometrical picture, applicable to all values of $N$. After listing the properties of this Hilbert space, we study the generalized coherent states that result when $ξ^N=0$, for $N \ge 2$. We also solve the generalized harmonic oscillator problem and derive generalized versions of the Hermite polynomials for general $N$. Some remarks are made to connect this study to the case of anyons. This study represents the first steps towards developing an anyonic field theory.
