Abstract:
As it is known, the closed inexact exterior form and associated closed dual form make up a differential-geometrical structure. Such a differential-geometrical structure describes a physical structure, namely, a pseudostructure on which conservation laws are fulfilled (A closed dual form describes a pseudostructure. And a closed exterior form, as it is known, describes a conservative quantity, since the differential of closed form is equal to zero). It has been shown that closed inexact exterior forms, which describe physical structures, are obtained from the equations of mathematical physics. This process proceeds spontaneously under realization of any degrees of freedom of the material medium described. Such a process describes an emergence of physical structures and this is accompanied by an appearance of observed formations such as fluctuations, waves, turbulent pulsations and so on.

Abstract:
It has been shown that the first
principle of thermodynamics follows from the conservation laws for energy and
linear momentum. And the second principle of thermodynamics follows from the
first principle of thermodynamics under realization of the integrating factor
(namely, temperature) and is a conservation law.The significance of
the first principle of thermodynamics consists in the fact that it specifies
the thermodynamic system state, which depends on interaction between conservation
laws and is non-equilibrium due to a non-commutativity of conservation laws.
The realization of the second principle of thermodynamics points to a
transition of the thermodynamic system state into a locally-equilibrium state. Phase transitions are examples of such transitions.

Abstract:
From the equations of conservation laws for energy, linear momentum, angular momentum and mass the evolutionary relation in differential forms follows. This relation connects the differential of entropy and the skew-symmetric form, whose coefficients depend on the characteristics of gas-dynamic system and the external actions. The evolutionary relation turns out to be nonidentical that is explained by the noncommutativity of conservation laws. The properties of such nonidentical relation (selfvariation, degenerate transformation) enable one to disclose the mechanism of evolutionary processes in gas-dynamic system that are accompanied by origination of vorticity and turbulence. In this case the intensity of vorticity and turbulence is defined by the commutator on unclosed skew-symmetric form in the nonidentical evolutionary relation.

Abstract:
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 obtained from the equations modelling conservation (balance) laws for material sistems (material media). The process of obtaining closed exterior forms demonstrates the connection between field-theory equations and the equations for material sistems and points to the fact that the foundations of field theories must be conditioned by the properties of equations conservation laws for material sistems.

Abstract:
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 those that claim the existence of conservative physical quantities or objects. These are conservation laws for physical fields. In contrast to that in physics (and mechanics) of material systems the concept of "conservation laws" relates to conservation laws for energy, linear momentum, angular momentum, and mass that establish the balance between the change of physical quantities and external action. In the paper presented it is proved that there exist a connection between of conservation laws for physical fields and those for material systems. This points to the fact that physical fields are connected with material systems. Such results has an unique significance for field theories. This enables one to substantiate many basic principles of field theories, such as, for example, the unity of existing field theories and the causality. The specific feature of field theory equations, namely, their connection to the equations for material systems, is elicited. Such results have been obtained by using skew-symmetric differential forms, which reflect the properties of conservation laws.

Abstract:
Physical meaning and a duality of concepts of wave function, action functional, entropy, the Pointing vector, the Einstein tensor and so on can be disclosed by investigating the state of material systems such as thermodynamic and gas dynamic systems, systems of charged particles, cosmologic systems and others. These concepts play a same role in mathematical physics. They are quantities that specify a state of material systems and also characteristics of physical fields. The duality of these concepts reveals in the fact that they can at once be both functionals and state functions or potentials. As functionals they are defined on nonintegrable manifold (for example, on tangent one), and as a state function they are defined on integrable manifold (for example, on cotangent one). The transition from functionals to state functions dicribes the mechanism of physical structure origination. The properties of these concepts can be studied by the example of entropy and action. The role of these concepts in mathematical physics and field theory will be demonstrated. Such results have been obtained by using skew-symmetric forms. In addition to exterior forms, the skew-symmetric forms, which are obtained from differential equations and, in distinction to exterior forms, are evolutionary ones and are defined on nonintegrable manifolds, were used.

Abstract:
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 means that the closed form is the conservative quantity, and this corresponds to the conservation laws for physical fields. In the present work a role in field theory of the exterior forms, which correspond to the conservation laws for the material systems is clarified. These forms are defined on the accompanying nondifferentiable manifolds, and hense, they are not closed. Transition from the forms, which correspond to the conservation laws for the material systems, to those, which correspond to the conservation laws for physical fields (it is possible under the degenerate transform), describe a mechanism of origin of the physical structures that format physical fields. In the work it is shown that the physical structures are generated by the material systems in the evolutionary process. In Appendices we give an analysis of the principles of thermodinamics and equations of the electromagnetic field. A role of the conservation laws in formation of the pseudometric and metric spaces is also shown.

Abstract:
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 structures, which the physical fields and relevant manifolds are constructed of. These are conservation laws for physical fields. 2. The conservation laws of energy, linear and angular momentum, and mass. These laws are conservation laws for material systems (material media). They establish a balance between changes of physical quantities and external actions. Such conservation laws can be called as balance ones. It has been shown that the exact and balance conservation laws execute a relation between the physical structures, which form physical fields, and material systems. The physical structures, to which the exact conservation laws correspond, are generated by material systems in the evolutionary processes, whose moving force is the noncommutativity of the balance conservation laws. These results are obtained with the help of the mathematical apparatus of skew-symmetric differential forms.

Abstract:
In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity and the corresponding external action), turn out to be noncommutative. The noncommutativity of the conservation laws that leads to an emergence of internal forces and an appearance of the nonequilibrium is a cause of development of instability in material media (material systems). These results were obtained with the help of the mathematical apparatus of skew-symmetric differential forms. To study the causes of developing instability it is necessary to inspect the evolutionary relation obtained from equations of the balance conservation laws and to analyze the differential form commutator that enters into this relation. In the present work the method of skew-symmetric differential forms has been applied in study of the thermodynamical and gas dynamical systems. It was shown that the principle of thermodynamics follows from two conservation laws, namely, the balance conservation laws for energy and linear momentum. In this case the second principle of thermodynamics, from which the state function (which specifies a state of the thermodynamical system) is obtained, follows from the first principle. A mechanism of development of instability in gas dynamical systems is described and there are explained such processes as emergence of waves, vortices, turbulent pulsations and so on.

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.