2 research outputs found
Finsler Geometries from Topological Electromagnetism
We analyse the Finsler geometries of the kinematic space of spinless and
spinning electrically charged particles in an external Ra\~{n}ada field. We
consider the most general actions that are invariant under the Lorentz,
electromagnetic gauge and reparametrization transformations. The Finsler
geometries form a set parametrized by the gauge fields in each case. We give a
simple method to calculate the fundamental objects of the Finsler geometry of
the kinematic space of a particle in a generic electromagnetic field. Then we
apply this method to calculate the geodesic equations of the spinless and
spinning particles. Also, we show that the electromagnetic duality in the
Ra\~{n}ada background induces a simple dual map in the set of Finsler
geometries. The duality map has a simple interpretation in terms of an
electrically charged particle that interacts with the electromagnetic potential
and a magnetically charged particle that interacts with the dual
magnetoelectric potential. We exemplify the action of the duality map by
calculating the dual geodesic equation.Comment: 24 page