Coherent state quantization of paragrassmann algebras

TL;DR

This paper introduces a method for quantizing paragrassmann algebras using coherent states, resulting in finite-dimensional matrix representations that realize deformed Weyl-Heisenberg algebras and offer insights into operator mean values.

Contribution

It presents a novel coherent state quantization approach for paragrassmann algebras, leading to finite matrix representations and new understanding of their algebraic structure.

Findings

Operators are represented as finite matrices.

The algebra realizes a deformed Weyl-Heisenberg algebra.

Mean values in coherent states reveal new properties.

Abstract

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators lead to interesting conclusions.