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Approaches to general field theory (The method of skew-symmetric differential forms)

L. I. Petrova
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Abstract

The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical fields. It is possible to classify physical fields and interactions. So, the (0-form) corresponds to the strong interaction, the (1-form) corresponds to the weak interaction, the (2-form) coorresponds to the electromagnetic interaction, and the (3-form) corresponds to the gravitational interaction. This is the basis of unified field theory. As a general field theory it can be a theory, which not only decribes possible physical fields and relation between them, but also discloses a mechanism of forming physical fields and the causality of such processes. It occurs that as the basis of such a theory it can become the theory of skew-symmetric differential forms defined on manifolds with unclosed metric forms. These differential forms, which were named the evolutionary ones, reflrect the properties of the conservation laws for material media (the balance conservation laws for energy, linear and angular momentum, and mass) and disclose a mechanism of the evolutionary processes in material media. It is in such processes the physical structures that form physical fields originate. The theory of exterior and evolutionary skew-symmetric differential forms discloses the causality of physical processes, establishes a relation between physical fields and material media and allows to introduce a classification of physical fields and interactions.

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L. I. Petrova. 2003-11-20. Approaches to general field theory (The method of skew-symmetric differential forms). https://arxiv.org/abs/math-ph/0311030

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