Finsler Geometries from Topological Electromagnetism
arXiv:2006.03865 · doi:10.1140/epjc/s10052-020-8123-3
Abstract
We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Rañada 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 Rañada 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.
arXiv comment24 pages
References in corpus (17)
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- Knots and Particles
- Riemann-Finsler geometry and Lorentz-violating kinematics
- Classical-physics applications for Finsler space
- Knotted solutions, from electromagnetism to fluid dynamics
- Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
- New knotted solutions of Maxwell's equations
- Knotted solutions for linear and nonlinear theories: electromagnetism and fluid dynamics
- Linked and Knotted Gravitational Radiation
- Motion of charged particles in an electromagnetic knot
- A new construction of rational electromagnetic knots
- Knotted optical vortices in exact solutions to Maxwell's equations
- On a remarkable electromagnetic field in the Einstein Universe
- Nonlinear electrodynamics is skilled with knots
- On the existence of the field line solutions of the Einstein-Maxwell equations
- On spacetime foliations and electromagnetic knots
- Lagrangian formulation, generalizations and quantization of null Maxwell's knots