Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly considered.

Geometric formulation of Lagrangian relativistic mechanics in the terms of jets of one-dimensional submanifolds is generalized to Lagrangian theory of submanifolds of arbitrary dimension.

We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular field theory on smooth… Expand

This work incorporates three modern aspects of mathematical physics: the jet methods in differntial geometry, the Lagrangian formalism on jet manifolds and the multimomentum approach to the… Expand

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… Expand

We analyse exhaustively the geometric formulations of the time-dependent regular dynamical systems, both the Hamiltonian and the Lagrangian formalisms. We study the equivalence between the different… Expand

It is shown that a natural extension of canonical Heisenberg-picture quantum mechanics is well defined and can be used to describe the "non-Schr\"odinger regime," in which a fundamental time variable is not defined.Expand