Skew-symmetric differential forms in mathematics, mathematical physics and field theoryкнига

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[1] Petrova L. I. Skew-symmetric differential forms in mathematics, mathematical physics and field theory. — URSS(Moscow) Moscow, 2013. — 234 p. 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. In present paper, firstly, the role of closed exterior skew-symmetric differential forms is illustrated, and, secondly, it is shown that there exist evolutionary skew-symmetric differential forms that generate closed exterior differential forms. The process of extracting closed exterior forms from evolutionary forms enables one to describe discrete transitions, quantum jumps, the generation of various structures, origination of such formations as waves, vortices and so on. In none of other mathematical formalisms such proceses can be described since their description includes degenerate transformations and transitions from nonintegrable manifolds to integrable ones.

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