On the structure of cohomological models of electrodynamics and general relativity

Abstract

In the present paper, we take case of a complex scalar field on a Riemannian manifold and study differential geometry and cohomological way to construct field theory Lagrangians. The total Lagrangian of the model is proposed as 4-form on Riemannian manifold. To this end, we use inner product of differential (p, q)-forms and Hodge star operators. It is shown that actions, including that for gravity, can be represented in quadratic forms of fields of matter and basic tetrad fields. Our study is limited to the case of the Levi-Civita metric. We stress some features arisen within the approach regarding nil potency property. Within the model, Klein-Gordon, Maxwell and general relativity actions have been reproduced.