Hadamard States for the Vector Potential on Asymptotically Flat Spacetimes

TL;DR

This paper develops a covariant quantization scheme for the vector potential on asymptotically flat spacetimes, establishing a bulk-to-boundary correspondence to identify a distinguished Hadamard state.

Contribution

It introduces a new covariant quantization framework for the vector potential and applies a bulk-to-boundary method to find a natural ground state on asymptotically flat backgrounds.

Findings

Established a conformal quantum field theory for the vector potential.

Constructed a distinguished Hadamard state using bulk-to-boundary correspondence.

Applicable to a large class of asymptotically flat spacetimes.

Abstract

We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary correspondence procedure in order to identify for the underlying field algebra a distinguished ground state which is of Hadamard form.