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.

References

SHOWING 1-10 OF 10 REFERENCES
Lagrangian and Hamiltonian dynamics of submanifolds
Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular
Advanced Classical Field Theory
Differential Calculus on Fiber Bundles Lagrangian Theory on Fiber Bundles Covariant Hamiltonian Field Theory Grassmann-Graded Lagrangian Theory Lagrangian BRST Theory Gauge Theory on Principal Fiber
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
Geometric And Algebraic Topological Methods In Quantum Mechanics
Commutative Geometry Classical Hamiltonian Systems Algebraic Quantization Geometry of Algebraic Quantization Geometric Quantization Supergeometry Deformation Quantization Non-Commutative Geometry
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
Quantum evolving constants. Reply to "Comment on 'Time in quantum gravity: An hypothesis' "
  • Rovelli
  • Physics
    Physical review. D, Particles and fields
  • 1991
Hajicek's interesting and valuable comments on the time hypothesis bear on the difficulties of the quantization process of a given classical theory, but they do not bear on the general issue of the
Gauge Mechanics (World Scientific, Singapore)
  • 1998
Methods of differential geometry in analytical mechanics