Lagrangian dynamics of submanifolds. Relativistic mechanics
@article{Sardanashvily2011LagrangianDO, title={Lagrangian dynamics of submanifolds. Relativistic mechanics}, author={Gennadi A Sardanashvily}, journal={arXiv: Mathematical Physics}, year={2011} }
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.
4 Citations
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References
SHOWING 1-10 OF 14 REFERENCES
Relativistic mechanics in a general setting
- Physics
- 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…
Geometric Formulation of Classical and Quantum Mechanics
- Physics, Mathematics
- 2010
Dynamic Equations Lagrangian Mechanics Hamiltonian Mechanics Algebraic Quantization Geometric Quantization Constrained Systems Integrable Hamiltonian Systems Jacobi Fields Systems with Parameters:…
New Lagrangian and Hamiltonian Methods in Field Theory
- Physics
- 1997
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…
Geometrical Setting of Time-Dependent Regular Systems:. Alternative Models.
- Mathematics, Physics
- 1991
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…
Hamiltonian time-dependent mechanics
- Physics
- 1998
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…
On the notion of gauge symmetries of generic Lagrangian field theory
- Mathematics
- 2009
General Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Its nontrivial reducible gauge symmetries and their algebra are defined in this very general setting by…
String theory.
- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 1998
The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom.
String theory
- MathematicsJournal of Symbolic Logic
- 1974
Abstract For each n > 0, two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the…
Some variations on the notion of connection
- Mathematics
- 1994
Distributions on manifolds are studied in terms of jets of submanifolds and are interpreted as «pre-connections» or «almost-fibrings»; the associated differential calculus is developed in detail. A…
Advanced Classical Field Theory
- Physics, Mathematics
- 2009
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…