Gravity and Duality between Coordinates and Matter Fields

TL;DR

This paper explores a duality between spacetime coordinates and matter fields, using solutions of the Klein-Gordon equation to parametrize spacetime geometry and analyze their interrelation in quantum field theory.

Contribution

It introduces a novel parametrization of spacetime metrics and connections based on duality with Klein-Gordon solutions, linking coordinates and quantum fields.

Findings

Spacetime components expressed via wave functions and prepotentials.

Duality between coordinates and quantum fields established.

Reparametrization of Einstein equations in this framework.

Abstract

We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metric in this later reparametrization.