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

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.

Automated summary

We argue that the same techniques used to evolve the Cauchy problem for first-order derivative self-interacting scalar fields can also be applied to self-interacting vector fields, avoiding the issues and pathologies recently found in the literature.