Coherent states with complex functions

TL;DR

This paper introduces new classes of coherent states by replacing the complex parameter with functions like iterates and elementary functions, exploring their algebraic structures and associated Hilbert spaces.

Contribution

It presents novel classes of coherent states based on functional replacements of the complex parameter, analyzing their algebraic and Hilbert space properties.

Findings

Some classes do not generate generalized oscillator algebras.

A reproducing kernel Hilbert space is constructed for each class.

The approach broadens the framework of coherent states beyond traditional complex parameters.

Abstract

The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states.