Non-Symplectic Geometry of First Order Time-Dependent Mechanics

Details Non-Symplectic Geometry of First Order Time-Dependent Mechanics Non-Symplectic Geometry of First Order Time-Dependent Mechanics

1997-10-04

arxiv.org/abs/dg-ga/9710003v1

Mathematics

Differential Geometry

24 pages, LaTeX

Scientific paper

The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ 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 $Y\to R$ whose fibration $Y\to M$ 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 $Y\to R$ is not fixed.

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