Gauge-invariant theories and higher-degree forms

Abstract

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.

24 pages, no figures, added references

References in corpus (4)

• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)
• Differential geometry construction of anomalies and topological invariants in various dimensions
• Propagating modes of non-Abelian tensor gauge field of second rank