Symplectic structures and globally hyperbolic spacetimes

TL;DR

This paper constructs symplectic structures directly on orientable globally hyperbolic 4D Lorentzian manifolds and discusses their geometric quantisation, advancing the mathematical framework for understanding spacetime in physics.

Contribution

It introduces a novel construction of symplectic structures on the manifold itself, not relying on cotangent bundles, and explores their geometric quantisation.

Findings

Symplectic structures are constructed directly on the manifold.

Discussion on geometric quantisation of these structures.

Provides a new mathematical framework for spacetime analysis.

Abstract

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also includes a discussion about their geometric quantisation.