CPN Models in General Coordinates

TL;DR

This paper analyzes complex projective space models using general coordinates, revealing their metric structures and comparing different coordinate systems, with specific focus on CP2 and CP4.

Contribution

It provides closed-form expressions for CPN models in arbitrary coordinates, enhancing understanding of their geometric properties and metric forms.

Findings

Retrieval of stereographic coordinates shows hermitian metric form for CP2

Comparison with Fubini-Study metric for CP4

Explicit coordinate expressions for CPN models

Abstract

An analysis of CPN models is given in terms of general coordinates or arbitrary interpolating fields.Only closed expressions made from simple functions are involved.Special attention is given to CP2 and CP4. In the first of these the retrieval of stereographic coordinates reveals the hermitian form of the metric. A similar analysis for the latter case allows comparison with the Fubini-Study metric.