Geometry via coherent states

TL;DR

This paper demonstrates how coherent states can be used to derive various geometric objects and properties, linking quantum concepts with classical differential geometry.

Contribution

It introduces a novel approach using coherent states to compute and analyze fundamental geometric structures and invariants.

Findings

Derived geodesics, conjugate and cut loci using coherent states

Connected Calabi's diastasis and domain to quantum states

Linked Euler-Poincaré characteristic and Borel-Morse cells to coherent state analysis

Abstract

It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the Euler-Poincar\'e characteristic, the number of Borel-Morse cells, the Kodaira embedding theorem.