Differential Geometry of Time-Dependent Mechanics

Simple item page
dc.creatorGiachetta, G.
dc.creatorMangiarotti, L.
dc.creatorSardanashvily, G.
dc.date1997-02-25
dc.date.accessioned2026-07-07T09:12:59Z
dc.date.available2026-07-07T09:12:59Z
dc.descriptionThe usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical transformations. Our goal is to formulate time-dependent mechanics in gauge-invariant form, i.e., independently of any reference frame. The main ingredient in this formulation is a connection on the bundle $Y\to R$ which describes an arbitrary reference frame. We emphasize the following peculiarities of this approach to time-dependent mechanics. A phase space does not admit any canonical contact or presymplectic structure which would be preserved under reference frame transformations, whereas the canonical Poisson structure is degenerate. A Hamiltonian fails to be a function on a phase space. In particular, it can not participate in a Poisson bracket so that the evolution equation is not reduced to the Poisson bracket. This fact becomes relevant to the quantization procedure. Hamiltonian and Lagrangian formulations of time-dependent mechanics are not equivalent. A degenerate Lagrangian admits a set of associated Hamiltonians, none of which describes the whole mechanical system given by this Lagrangian.
dc.description79 pages, Latex
dc.identifierhttps://arxiv.org/abs/dg-ga/9702020
dc.identifierhttp://arxiv.org/abs/dg-ga/9702020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152213
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleDifferential Geometry of Time-Dependent Mechanics
dc.typetext

Files

Collections

arXiv