U(1) Gauge Potentials on de Sitter Spacetime

TL;DR

This paper constructs the U(1) gauge potential on de Sitter spacetime using the Verma module of the Lie algebra and demonstrates that electromagnetic fields cannot be source-free in this background.

Contribution

It introduces a novel representation of U(1) gauge potentials on de Sitter space via the Verma module of a9(1,4), revealing new insights into electromagnetic fields in curved spacetime.

Findings

Electromagnetic fields on de Sitter space cannot be source-free.

The Verma module provides a mathematical framework for gauge potentials.

The work links representation theory with gauge field properties in curved spacetime.

Abstract

The smooth 1-form Verma module of $\mathfrak{so}(1,4)$ is acquired, which can be regarded as the U(1) gauge potential on de Sitter spacetime. It is shown that electromagnetic fields could not be source free on de Sitter background.