Generalizations of Perelomov's identity on the completeness of coherent states

TL;DR

This paper proves and generalizes Perelomov's identity for 2D lattices, extending its applicability to non-origin-centered lattices and magnetic wave functions in different gauges, enhancing understanding of coherent states.

Contribution

The authors prove Perelomov's identity for arbitrary 2D lattices and extend it to non-origin-centered cases with magnetic wave function similarities, broadening its theoretical scope.

Findings

Proof of Perelomov's identity for arbitrary 2D lattices

Generalization to non-origin lattice sites

Application to magnetic wave functions in uniaxial gauge

Abstract

We proof the Perelomov identity for arbitrary 2D lattices using Fourier transformation. We further generalize it to situations where the origin does not coincide with a lattice site, and where the form of the exponential factor is reminiscent of magnetic wave functions in uniaxial rather than symmetric gauge.