Five-Dimensional Tangent Vectors in Space-Time

Abstract

This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit greater than that of the manifold. Like ordinary tangent vectors, the considered five-dimensional vectors and the tensors constructed out of them can be used for describing certain local quantities and in this capacity find direct application in physics. For example, such familiar physical quantities as the stress-energy and angular momentum tensors prove to be parts of a single five-tensor. In this paper I describe several different mathematical definitions of five-dimensional tangent vectors, discuss their basic algebraic and differential properties, and speak about their possible application in the theory of gravity and in gauge theories.