Causality and classical dispersion relations

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.

Comments: 16 pages, 1 figure. v2: reference added, small clarifications. v3: reference added, published version