Skew-symmetric differential forms possess unique capabilities that manifest themselves in various branches of mathematics and mathematical physics. The invariant properties of closed exterior skew-symmetric differential forms lie at the basis of practically all invariant mathematical and physical formalisms. Closed exterior forms, whose properties correspond to conservation laws, explicitly or implicitly manifest themselves essentially in all formalisms of field theory. In the present work, firstly, the role of closed exterior skew-symmetric differential forms in mathematics, mathematical physics and field theory is illustrated, and, secondly, it is shown that there exist skew-symmetric differential forms that generate closed exterior differential forms. These skew-symmetric forms are derived from differential equations and possess evolutionary properties. The process of extracting closed exterior forms from evolutionary forms enables one to describe discrete transitions, quantum...
Skew-symmetric differential forms possess unique capabilities that manifest themselves in various branches of mathematics and mathematical physics. The invariant properties of closed exterior skew-symmetric differential forms lie at the basis of practically all invariant mathematical and physical formalisms. Closed exterior forms, whose properties correspond to conservation laws, explicitly or implicitly manifest themselves essentially in all formalisms of field theory. In the present work, firstly, the role of closed exterior skew-symmetric differential forms in mathematics, mathematical physics and field theory is illustrated, and, secondly, it is shown that there exist skew-symmetric differential forms that generate closed exterior differential forms. These skew-symmetric forms are derived from differential equations and possess evolutionary properties. The process of extracting closed exterior forms from evolutionary forms enables one to describe discrete transitions, quantum...
