Causality and classical dispersion relations

TL;DR

This paper investigates how relativistic causality and stability principles impose constraints on the dispersion relations of classical systems, especially in relativistic hydrodynamics, at high momenta.

Contribution

It derives causality and stability constraints on dispersion relations for systems described by finite PDEs, advancing understanding of relativistic hydrodynamics.

Findings

Causality constrains high-momentum dispersion relations.

Covariant stability imposes bounds on excitation frequencies.

Results apply to classical relativistic systems with finite PDE descriptions.

Abstract

We explore the consequences of relativistic causality and covariant stability for short-wavelength dispersion relations in classical systems. For excitations described by a finite number of partial differential equations, as is the case in relativistic hydrodynamics, we give causality and covariant stability constraints on the excitation's frequency at large momenta.