An invariant analytic orthonormalization procedure with an application to coherent states

TL;DR

This paper introduces a general method for constructing orthonormal sets of vectors that remain stable under specific unitary operations, with applications to creating coherent-like states and analyzing conditions for their formation.

Contribution

It presents a novel invariant orthonormalization procedure applicable to sets of vectors generated by unitary operators, including coherent states.

Findings

The procedure produces orthonormal sets stable under given unitary operators.

It can generate coherent-like vectors under certain lattice spacing conditions.

The method is demonstrated through several illustrative examples.

Abstract

We discuss a general strategy which produces an orthonormal set of vectors, stable under the action of a given set of unitary operators $A_j$, $j=1,2,...,n$, starting from a fixed normalized vector in $\Hil$ and from a set of unitary operators. We discuss several examples of this procedure and, in particular, we show how a set of {\em coherent-like} vectors can be produced and in which condition over the lattice spacing this can be done.