Kaluza-Klein Theory as a Dynamics in a Dual Geometry

Abstract

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flow on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits in space-time associated with a relativistic system. One can study the consequences on the geometry of the introduction of electromagnetic interaction. We find that resulting geometrical structure in the dual space is that of Kaluza and Klein.

18 pages, no figures

References in corpus (2)

• On the geometry of Hamiltonian chaos
• Induced current and redefinition of electric and magnetic fields from non-compact Kaluza-Klein theory: An experimental signature of the fifth dimension

Cited by in corpus (6)

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• Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS
• Local Metric with Parameterized Evolution
• $N\ge 2$ Particles in the Framework of TeVeS
• Criterion for Stability of a Special Relativistically Covariant Dynamical System
• An Underlying Geometrical Manifold for Hamiltonian Mechanics