Relativistic mechanics in a general setting

@inproceedings{GSardanashvily2010RelativisticMI,
  title={Relativistic mechanics in a general setting},
  author={G.Sardanashvily},
  year={2010}
}
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. 

Lagrangian dynamics of submanifolds. Relativistic mechanics

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.

Fibre bundle formulation of time-dependent mechanics

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

References

SHOWING 1-9 OF 9 REFERENCES

New Lagrangian and Hamiltonian Methods in Field Theory

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

Hamiltonian time-dependent mechanics

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

Geometrical Setting of Time-Dependent Regular Systems:. Alternative Models.

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

Time in quantum gravity: An hypothesis.

  • Rovelli
  • Physics
    Physical review. D, Particles and fields
  • 1991
TLDR
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.

Gauge Mechanics (World Scientific, Singapore)

  • 1998

Methods of differential geometry in analytical mechanics

Lagrangian and Hamiltonian dynamics of submanifolds,arXiv: math-ph/0604066

  • 2006

Geometric and Topological Algebraic Methods in Quantum Mechanics

  • 2005