Alexander Krasulin. Five-Dimensional Tangent Vectors in Space-Time: IV. Generalization of Exterior Calculus

Natural Sciences / Mathematics / Geometry

Submitted on: Sep 25, 2012, 12:46:58

Description: This part of the series is devoted to the generalization of exterior differential calculus. I give definition to the integral of a five-vector form over a limited space-time volume of appropriate dimension; extend the notion of the exterior derivative to the case of five-vector forms; and formulate the corresponding analogs of the generalized Stokes theorem and of the Poincare theorem about closed forms. I then consider the five-vector generalization of the exterior derivative itself; prove a statement similar to the Poincare theorem; define the corresponding five-vector generalization of flux; and derive the analog of the formula for integration by parts. I illustrate the ideas developed in this paper by reformulating the Lagrange formalism for classical scalar fields in terms of five-vector forms. In conclusion, I briefly discuss the five-vector analog of the Levi-Civita tensor and dual forms.

The full-text article has been published in the "IntellectualArchive" journal , Vol.1, Num.5, September 2012, ISSN 1929-4700.