Extending coherent state transforms to Clifford analysis

TL;DR

This paper extends the Segal-Bargmann coherent state transform to Clifford analysis, specifically to slice monogenic and axial monogenic functions, exploring their properties and connections to quantum mechanics.

Contribution

It introduces two novel extensions of the coherent state transform to Clifford analysis and investigates their mathematical and physical properties.

Findings

Transforms relate via the dual Radon transform

Representation theoretic analysis conducted

Connections to quantum mechanics explored

Abstract

We introduce two extensions of the Segal-Bargmann coherent state transform from $L^2({\mathbb R},dx)$ to Hilbert spaces of slice monogenic and axial monogenic functions and study their properties. These two transforms are related by the dual Radon transform. Representation theoretic and quantum mechanical aspects of the new representations are studied.