相关论文: Approaches to general field theory (The method of …
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one…
A role of skew-symmetric differential forms in mathematical physics relates to the fact that they reflect the properties of conservation laws. The closed exterior forms correspond to the conservation laws for physical fields, whereas the…
In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of…
At present the theory of skew-symmetric exterior differential forms has been developed. The closed exterior forms possess the invariant properties that are of great importance. The operators of the exterior form theory lie at the basis of…
A role of the exterior differential forms in field theory is connected with a fact that they reflect properties of the conservation laws. In field theory a role of the closed exterior forms is well known. A condition of closure of the form…
Evolutionary forms are skew-symmetric differential forms the basis of which, as opposed to exterior forms, are deforming manifolds (with unclosed metric forms). Such differential forms arise when describing physical processes. A specific…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a…
The existing field theories are based on the properties of closed exterior forms, which correspond to conservation laws for physical fields. In the present paper it is shown that closed exterior forms corresponding to field theories are…
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the…
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…
Skew-symmetric differential forms play an unique role in mathematics and mathematical physics. This relates to the fact that closed exterior skew-symmetric differential forms are invariants. The concept of "Exterior differential forms" was…
Skew-symmetric forms possess unique capabilities. The properties of closed exterior and dual forms, namely, invariance, covariance, conjugacy and duality, either explicitly or implicitly appear in all invariant mathematical formalisms. This…
Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first…
Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of "conservation laws" has a different meaning. In field theory "conservation laws" are…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
It is shown that there is a correspondence between field theory equations such as the Dirac, Shr\H{o}dinger, Maxwell, Einstein equations and closed exterior forms of a certain degree. In this case, the Dirac and Shr\H{o}dinger equations for…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
Modern theories of fundamental interactions describe strong, electromagnetic and weak interactions as quantum field theories with certain kinds of embedded internal symmetries called `gauge symmetries'. This article introduces quantum field…