About the Overcompleteness of Coherent State Systems with a Line Bundles Viewpoint

TL;DR

This paper examines the overcompleteness of coherent state systems using a geometric approach involving holomorphic line bundles, and applies this to analyze degeneracy in the lowest Landau level.

Contribution

It introduces a geometric framework for analyzing overcomplete coherent state systems via holomorphic line bundles, extending traditional lattice-based methods.

Findings

Provides a geometric interpretation of overcompleteness

Evaluates degeneracy in the lowest Landau level

Classifies coherent state systems using line bundle properties

Abstract

Standart Coherent State Systems have an analysis based on lattices (von Neumann's lattices) in terms of wich they are classified, looking at the size of the minimun cell, by: complete, overcomplete and not complete. In this work we analize overcomplete systems with a geometrical viewpoint (holomorphic line-budles). We apply the method to evaluate the degeneracy of the lowest Landau level.