Localization in the Rindler Wedge

TL;DR

This paper explores how charged particles in quantum electrodynamics create photon clouds that break Lorentz symmetry, affecting localization of observables in the Rindler wedge and potentially impacting black hole information paradox discussions.

Contribution

It demonstrates that charged particles induce a non-trivial photon cloud leading to Lorentz symmetry breaking and affects localization properties in quantum field theory.

Findings

Lorentz boost generators diverge in charged particle states

Photon clouds prevent localization of observables in the Rindler wedge

Implications for black hole information loss paradox

Abstract

One of the striking features of QED is that charged particles create a coherent cloud of photons. The resultant coherent state vectors of photons generate a non-trivial representation of the localized algebra of observables that do not support a representation of the Lorentz group: Lorentz symmetry is spontaneously broken. We show in particular that Lorentz boost generators diverge in this representation, a result shown also in [1] (See also [2]). Localization of observables, for example in the Rindler wedge, uses Poincar\'e invariance in an essential way [3]. Hence in the presence of charged fields, the photon observables cannot be localized in the Rindler wedge. These observations may have a bearing on the black hole information loss paradox, as the physics in the exterior of the black hole has points of resemblance to that in the Rindler wedge.