Open AccessON THE STRUCTURE OF COHOMOLOGICAL MODELS OF ELECTRODYNAMICS AND GENERAL RELATIVITY
Author(s) -
V.V. Arkhipov V.V.
Publication year - 2020
Publication title -
eurasian physical technical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.194
H-Index - 2
eISSN - 2413-2179
pISSN - 1811-1165
DOI - 10.31489/2020no2/146-152
Subject(s) - tetrad , hodge dual , general relativity , riemannian geometry , manifold (fluid mechanics) , differential geometry , mathematics , theoretical physics , pure mathematics , hodge theory , scalar (mathematics) , scalar curvature , differential form , theory of relativity , physics , mathematical physics , geometry , cohomology , engineering , mechanical engineering , curvature
In the present paper, we take case of a complex scalar field on a Riemannian manifold and study diff erential 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.