Localization of observables in the Rindler wedge

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 nontrivial 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 by Balachandran et al. [Eur. Phys. J. C 75, 89 (2015)] (see also the work by Balachandran et al. [Mod. Phys. Lett. A 28, 1350028 (2013)]. Localization of observables, for example in the Rindler wedge, uses Poincar\'e invariance in an essential way [Int. J. Geom. Methods Mod. Phys. 14, 1740008 (2017).]. 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.