Hamiltonian time-dependent mechanics

Abstract

The usual formulation of time-dependent mechanics implies a given splitting Y=R×M of an event space Y. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle Y→R, whose fibration Y→M is not fixed. Its phase space is the vertical cotangent bundle V*Y, provided with the canonical 3-form and the corresponding canonical Poisson structure. An event space of relativistic mechanics is a manifold Z whose fibration Z→R is not fixed.