Gauging away Physics

TL;DR

The paper critically examines a nonlocal gauge transformation proposed to remove infrared divergences in de Sitter space graviton propagators, highlighting issues with legitimacy and implications for similar methods in flat space QED.

Contribution

It demonstrates that the gauge transformation introduces anti-sources that alter the propagator equation, questioning the validity of removing infrared divergences via such transformations.

Findings

The transformation adds anti-sources in the far future.

It changes the propagator equation, affecting physical interpretations.

Similar anti-source methods could be misused in flat space QED.

Abstract

We consider the recent argument by Higuchi, Marolf and Morrison [1] that a nonlocal gauge transformation can be used to eliminate the infrared divergence of the graviton propagator, when evaluated in Bunch-Davies vacuum on the open coordinate submanifold of de Sitter space in transverse-traceless-synchronous gauge. Because the transformation is not local, the equal time commutator of undifferentiated fields no longer vanishes. From explicit examination of the Wightman function we demonstrate that the transformation adds anti-sources in the far future which cancel the bad infrared behavior but also change the propagator equation. The same problem exists in the localized version of the recent argument. Adding such anti-sources does not seem to be legitimate and could be used to eliminate the infrared divergence of the massless, minimally coupled scalar. The addition of such anti-sources in flat space QED could be effected by an almost identical gauge transformation, and would seem to eliminate the well known infrared divergences which occur in loop corrections to exclusive amplitudes.