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arXiv · 2005.04223

Coherent States and Generalized Hermite Polynomials for fractional statistics -- interpolating from fermions to bosons

Satish Ramakrishna
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Abstract

This article develops the algebraic structure that results from the $\theta$-commutator $\alpha \beta - e^{i \theta} \beta \alpha = 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 $\xi^N=0$, 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.

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Satish Ramakrishna. 2020-05-11. Coherent States and Generalized Hermite Polynomials for fractional statistics -- interpolating from fermions to bosons. https://doi.org/10.1063/5.0022407

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