Superluminal propagation from IR physics

TL;DR

This paper investigates wave propagation speeds, demonstrating that IR physics can influence superluminal phenomena and challenging the assumption that UV limits solely determine wave front velocities.

Contribution

It shows that IR physics can lead to superluminal wavefronts, even when UV phase velocities are luminal, highlighting the importance of IR effects in wave propagation.

Findings

Front velocities match UV phase velocities in parity-conserving theories with higher spatial derivatives.

Superluminal front velocities can occur due to IR or intermediate energy scale properties.

IR physics can significantly affect wave propagation speeds, not just UV physics.

Abstract

One may believe that front velocities of waves in a given theory coincide with the UV limit of phase velocities for any dispersion relations. This implies that IR physics is irrelevant to the discussion of propagation speed of waves. We first consider a theory that contains higher spatial derivatives in the wave equation and prove that front velocities coincide with the UV limit of phase velocities, at least, if parity is conserved. However, we also show that front velocities do not coincide with the UV limit of phase velocities in general dispersion relations. We explicitly give several examples in which front velocities are superluminal owing to an IR or intermediate energy scale property of dispersion relations even if the UV limit of phase velocities is luminal. Our finding conveys the important caution that not only UV physics but also IR physics can be significant to superluminality.