# Canonical, squeezed and fermionic coherent states in a right quaternionic Hilbert space with a left multiplication on it

## TL;DR

This paper explores the construction of various coherent states, including canonical, squeezed, and fermionic, within a right quaternionic Hilbert space using a left multiplication, highlighting the challenges posed by quaternion noncommutativity.

## Contribution

It introduces a framework for defining multiple classes of coherent states on quaternionic Hilbert spaces and discusses the limitations caused by quaternion noncommutativity.

## Key findings

- Canonical, squeezed, and fermionic coherent states can be defined with desired properties.
- Quaternion noncommutativity hinders the realization of certain squeezed states.
- The framework extends the understanding of quaternionic quantum states.

## Abstract

Using a left multiplication defined on a right quaternionic Hilbert space, we shall demonstrate that various classes of coherent states such as the canonical coherent states, pure squeezed states, fermionic coherent states can be defined with all the desired properties on a right quaternionic Hilbert space. Further, we shall also demonstrate squeezed states can be defined on the same Hilbert space, but the noncommutativity of quaternions prevents us in getting the desired results.