The quantum theory of the free Maxwell field on the de Sitter expanding universe

TL;DR

This paper develops a quantum theory for the free Maxwell field in de Sitter spacetime, introducing new energy eigenfunctions and demonstrating canonical quantization in this curved background.

Contribution

It introduces new plane wave solutions that are eigenfunctions of the energy operator and extends the quantization framework to the de Sitter universe.

Findings

Energy and momentum operators do not commute in de Sitter spacetime.

New energy eigenfunctions complete the solution set for the Maxwell field.

Canonical quantization of the electromagnetic potential is achieved in the Coulomb gauge.

Abstract

The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves solutions of the Maxwell equation which are eigenfunctions of the energy operator. Such particular solutions complete the theory in which only the solutions of given momentum were considered so far. The energy eigenfunctions can be obtained thanks to our new time-evolution picture proposed previously for the scalar and Dirac fields. Considering both these types of modes, it is shown that the second quantization of the free electromagnetic potential in the Coulomb gauge can be done in a canonical manner as in special relativity. The principal conserved one-particle operators associated to Killing vectors are derived, concentrating on the energy, momentum and total angular momentum operators.