General Couplings of Four Dimensional Maxwell-Klein-Gordon System: Global Existence

TL;DR

This paper proves the global existence of solutions for a generalized Maxwell-Klein-Gordon system in four-dimensional Minkowski spacetime, incorporating complex scalar fields on a Kähler manifold with various potentials and gauge couplings.

Contribution

It introduces a broad class of Maxwell-Klein-Gordon systems with general gauge couplings and scalar potentials, establishing their global well-posedness.

Findings

Global existence is proven for systems with bounded gauge couplings.

Results apply to polynomial, sine-Gordon, and Toda scalar potentials.

The analysis covers complex scalar fields on Kähler manifolds.

Abstract

In this paper, we consider the multi component fields interactions of the complex scalar fields and the electromagnetic fields (Maxwell-Klein-Gordon system) on four dimensional Minkowski spacetime with general gauge couplings and the scalar potential turned on. Moreover, the complex scalar fields span an internal manifold assumed to be K\"{a}hler. Then, by taking the K\"{a}hler potential to be bounded above $U(1)^N$ symmetric K\"{a}hler potential, the gauge couplings to be bounded functions, and the scalar potential to be the form of either polynomial, sine-Gordon, or Toda potential, we prove the global existence of the system.