Covariant Cherenkov Radiation and its Friction Force

TL;DR

This paper generalizes the Cherenkov radiation formula covariantly, derives the associated relativistic friction force, and discusses implications for photon spectra and high-energy collisions.

Contribution

It provides the first covariant derivation of Cherenkov radiation and the corresponding reaction force, extending classical results into a relativistic framework.

Findings

Derived a covariant Frank-Tamm formula for Cherenkov radiation.

Obtained a four-force orthogonal to particle four-velocity as a relativistic friction force.

Presented a photon emission spectrum dependent on medium properties.

Abstract

We derive the covariant generalization of the Frank-Tamm formula describing the Cherenkov radiation by a charged particle moving uniformly with a speed faster than the local speed of light within a homogeneous dielectric medium. We use our result to derive the covariant Cherenkov radiation reaction force and obtain a four-force explicitly orthogonal to particle four-velocity consistent with a relativistic friction force. We present the photon emission spectrum that is dependent primarily on the dielectric properties of the medium. We hint at a possible use of this work to interpret an excess of soft photons seen in relativistic hadron collisions.