# Covariant Response Theory and the Boost Transform of the Dielectric Tensor

## TL;DR

This paper demonstrates that modern microscopic electrodynamics inherently provides a Lorentz-covariant response theory, deriving the transformation laws of the conductivity and dielectric tensors under Lorentz boosts from first principles.

## Contribution

It clarifies the Lorentz transformation behavior of dielectric tensors within microscopic electrodynamics, resolving issues with classical Minkowski formulations.

## Key findings

- Derivation of the relativistic transformation of the microscopic conductivity tensor.
- First-principles derivation of the dielectric tensor's transformation law.
- Critique of Minkowski's classical electromagnetic constitutive laws.

## Abstract

After a short critique of the Minkowski formulae for the electromagnetic constitutive laws in moving media, we argue that in actual fact the problem of Lorentz-covariant electromagnetic response theory is automatically solved within the framework of modern microscopic electrodynamics of materials. As an illustration, we first rederive the well-known relativistic transformation behavior of the microscopic conductivity tensor. Thereafter, we deduce from first principles the transformation law of the wavevector- and frequency-dependent dielectric tensor under Lorentz boost transformations.