Quantum phase transition of infrared radiation

A bstract We describe a phase transition of infrared radiation, driven by quantum fluctuations, which takes place at the boundary of (the conformal diagram of) Minkowski spacetime. Specifically, we consider a family of states interpolating between the vacuum and the Kraus-Polley-Reents infravacuum. A state from this family can be imagined as a static source emitting flashes of infrared radiation in distant past. The flashes are in suitable squeezed states and the time intervals between them are controlled by a certain parameter r . For r < 0 the states are lightcone normal, thus physically indistinguishable from local excitations of the vacuum. They suffer from the usual infrared problems such as disintegration of the Bloch-Nordsieck S -matrix and rotational symmetry breaking by soft photon clouds. However, for r > 0 lightcone normality breaks down, the S -matrix is stabilized by the Kraus-Polley-Reents mechanism and the rotational symmetry is restored. We interpret these two situations as ordered ( r < 0) and disordered ( r > 0) phase of infrared radiation, and show that they can be distinguished by asymptotic fluctuations of the fields. We also determine the singular behaviour of some S -matrix elements near the critical point r = 0.