Classical non-relativistic mechanics and classical field theory are adequately formulated in geometric terms of fibre bundles Y->X where field theory and

*dim X>**1*in

*X=*in mechanics.**R**
Configuration space of a classical non-relativistic mechanics is a fibre bundle

*Y->*over the time axis**R****. Its velocity space is a first order jet manifold***R**JY*of*Y*. Its phase space is the vertical tangent bundle*VY*of*Y*. Connections on a fibre bundle*Y->*characterize non-relativistic reference frames.**R**
Geometric formulation of classical field theory is based on a representation of classical fields by sections of fibre bundles

*Y->X*where*dim X>1*. Their Lagrangians are densities on finite order jet manifolds of*Y*. Connections on*Y->X*also are fields, e.g., gauge fields which are sections of the first order jet bundle*JY->Y*. In a very general setting, in order to include odd fields, e.g., fermions and ghosts, field theory is formulated on a graded manifold whose body is a fibre bundle*Y->X*.
The formulation of relativistic mechanics generalizes that of non-relativistic mechanics. It is phrased in terms of one-dimensional submanifolds of a configuration space. In a case of two-dimensional submanifolds, we come to classical string theory.

**References:**

G.Giachetta, L.Mangiarotti, G.Sardanashvily, Advanced Classical Field Theory (WS, 2009)

G.Giachetta, L.Mangiarotti, G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (WS, 2010)

G.Sardanashvily, Fibre bundles, jet manifolds and Lagrangian theory. Lectures for theoreticians, arXiv: 0908.1886

G.Sardanashvily, Advanced mechanics. Mathematical introduction arXiv: 0911.0411

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