Aspects of time evolution in p-form field theories

Abstract

We show that higher form fields, specifically 2- and 3-forms in four spacetime dimensions, suffer from loss of hyperbolicity when they have self interaction. The equations of motion lose their wavelike characteristic in certain parts of the configuration space, and such problematic regions can be reached dynamically from healthy initial data. These findings are analogous to recent results for vector fields, which are equivalently 1-forms, however, the details of the pathology can be different for higher forms. We also show that the possibility of more than one self-interaction term in higher form fields leads to a variety in time evolution characteristics, where hyperbolicity is lost in different parts of the configuration space as the interaction changes.