Gauge-invariant theories and higher-degree forms

A free differential algebra is generalization of a Lie algebra in which the mathematical structure is extended by including of new Maurer-Cartan equations for higher-degree differential forms. In this article, we propose a generalization of the Chern-Weil theorem for free differential algebras containing only one p-form extension. This is achieved through a generalization of the covariant derivative, leading to an extension of the standard formula for Chern-Simons and transgression forms. We also study the possible existence of anomalies originated on this kind of structure. Some properties and particular cases are analyzed.

Automated summary

A free differential algebra extends the structure of a Lie algebra by including new Maurer-Cartan equations for higher-degree differential forms. This article proposes a generalization of the Chern-Weil theorem for free differential algebras with only one p-form extension, achieved through a generalization of the covariant derivative. The study also investigates the potential existence of anomalies and analyzes properties and particular cases.