Extending coherent state transforms to Clifford analysis

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.

Cited by in corpus (8)

• Segal-Bargmann-Fock modules of monogenic functions
• On the Bargmann-Fock-Fueter and Bergman-Fueter integral transforms
• Coherent State Transforms and the Weyl Equation in Clifford Analysis
• On the Bargmann-Radon transform in the monogenic setting
• The Cholewinski-Fock space in the Slice Hyperholomorphic Setting
• On the Mittag Leffler Bargmann (MLB) transform
• Clifford Algebra-valued Segal-Bargmann Transform and Taylor Isomorphism
• Segal-Bargmann transform for generalized partial-slice monogenic functions