On the construction of generalized Grassmann representatives of state vectors

TL;DR

This paper introduces a method using generalized Z_k-graded Grassmann variables to construct coherent states and their representatives for q-oscillator systems at roots of unity, expanding the mathematical framework for quantum state labeling.

Contribution

It presents a novel approach to constructing generalized Grassmann representatives of state vectors using Z_k-graded variables for q-oscillators at roots of unity.

Findings

Successful construction of coherent states with generalized Grassmann variables

Extension of state vector representation in q-oscillator systems

Potential applications in quantum state analysis

Abstract

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.