Coherent state quantization of paragrassmann algebras

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.

We provide an erratum where we improve upon our previous definition of odd paragrassmann algebras

References in corpus (3)

• A class of generalized complex Hermite polynomials
• Coherent state quantization of paragrassmann algebras
• Coherent state quantization of angle, time, and more irregular functions and distributions

Cited by in corpus (7)

• Coherent state quantization of paragrassmann algebras
• Action-angle coherent states for quantum systems with cylindric phase space
• Coherent states in Quantum Optics: An oriented overview
• Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement
• Paragrassmann Algebras as Quantum Spaces, Part II: Toeplitz Operators
• Coherent States for the Manin Plane via Toeplitz Quantization
• A Reproducing Kernel and Toeplitz Operators in the Quantum Plane