Classical electrodynamics on Snyder space

TL;DR

This paper develops a classical electrodynamics framework on Snyder space, a curved energy-momentum background, leading to finite self-energy for point charges and new insights into electromagnetic phenomena in non-zero curvature spaces.

Contribution

It introduces a formulation of electrodynamics on Snyder space, incorporating curvature into the energy-momentum background and redefining key concepts like integration and delta functions.

Findings

Finite self-energy for point charges.

Electromagnetic solutions in Snyder space resemble standard cases outside sources.

New definitions of integration measure and delta functions in curved energy-momentum space.

Abstract

A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and promoting the energy-momentum vector to belong to a constant (non-zero) curvature space. In particular, special emphasis is given to the definition of integration measure and generalized Dirac's delta function. Finally, simple physical problems as plane waves (solutions outside sources) and point charges are discussed in this context, where the self-energy of a point charge is shown to be finite.