A new approach to electromagnetism in anisotropic spaces

TL;DR

This paper extends classical electromagnetism equations to anisotropic (Finslerian) spaces using variational and exterior calculus methods, highlighting differences from traditional approaches.

Contribution

It introduces a novel variational and exterior calculus framework for electromagnetism in anisotropic spaces, differing from previous methods.

Findings

Electromagnetic tensors depend on space direction in anisotropic spaces

Derived generalized Maxwell equations for Finslerian geometries

Identified key differences from classical electromagnetism approaches

Abstract

Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical equations of electromagnetism to anisotropic (Finslerian) spaces. The results differ from the ones obtained by means of the known approach in [3], [4].