1997/10/04 by G. Sardanashvily, Sardanashvily, G.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9710003
24 pages, LaTeX
arxiv created 1997/10/04 · arxiv updated 2009/11/30
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 Y whose fibration Y→ R is not fixed.