The well-posedness of the Cauchy problem for self-interacting vector fields

TL;DR

This paper discusses the well-posedness of the Cauchy problem for self-interacting vector fields, showing that techniques used for scalar fields can be adapted to vector fields to avoid known issues.

Contribution

It demonstrates that methods used for scalar fields' Cauchy problem can be extended to vector fields, improving understanding of their evolution without requiring ultraviolet completion.

Findings

Techniques for scalar fields' Cauchy problem are applicable to vector fields.

Applying these methods avoids recent issues and pathologies in vector field evolution.

The approach enhances the theoretical foundation for self-interacting vector fields.

Abstract

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents the same well-posedness issues as for first-order derivative self-interacting scalar fields (often referred to as $k$-essence). For the latter, suitable strategies have been employed in the last few years to successfully evolve the Cauchy problem at the level of the infrared theory, without the need for an explicit ultraviolet completion. We argue that the very same techniques can also be applied to self-interacting vector fields, avoiding a number of issues and "pathologies" recently found in the literature.