Non-Symplectic Geometry of First Order Time-Dependent Mechanics

arXivdg-ga/9710003MaRDI QIDQ6467078

G. Sardanashvily

Publication date: 4 October 1997

Abstract: The usual formulation of time-dependent mechanics implies a given splitting $Y=RimesM$ 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 $YoR$ whose fibration $YoM$ 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 $YoR$ is not fixed.

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