Classical Phase Space from a Relativist’s Point of View

Abstract

A new formulation of phase space of classical mechanics is proposed based on a known four-dimensional formulation of the space-time. With space-time represented by a four-dimensional manifold S (with affine structure and stratified by Euclidean three dimensional spaces) the phase space $\bar \Gamma$ for a single particle is defined as the cotangent bundle of S. Thus $\bar \Gamma$ is an eight dimensional manifold and a vector bundle with symplectic structure and tensor fields transferred from S. Some remarks on the constants of motion are made. In the general case of a system with n degrees of freedom $\bar \Gamma$ is a manifold with 2n+2 dimensions.