Abstract
We consider two applications of the factorization of infrared dynamics in QED and gravity. The first is a redefinition of the Lorentz transformations that makes them commute with supertranslations. The other is the process of particle creation near a black hole horizon. For the latter we show that the emission of soft particles factors out of the S-matrix in the fixed-background approximation and to leading order in the soft limit. The factorization is implemented by dressing the incoming and outgoing asymptotic states with clouds of soft photons and soft gravitons. We find that while the soft photon cloud has no effect, the soft graviton cloud induces a phase shift in the Bogolyubov coefficients relating the incoming and outgoing modes. However, the flux of outgoing particles, given by the absolute value of the Bogolyubov coefficient, is insensitive to this phase.
Highlights
Instead show how to use the infrared factorization of dynamics induced by the infrared dressing to simplify the dynamics of the radiative degrees of freedom
The first is a redefinition of the Lorentz transformations that makes them commute with supertranslations
The other is the process of particle creation near a black hole horizon
Summary
We use the results of [15] to define a quantum canonical transformations of the operator algebra that maps the standard asymptotic local fields into “dressed” fields that commute with the soft charges. In the BMS case the transformation acts on all radiative degrees of freedom, including the Bondi news, as a translation (see [15] and section 4). The charges Q±lm were defined recently at spacelike infinity, where conservation is essentially ensured by definition [29,30,31]; it is plausible that soft gravitons and photons could be likewise defined at spacelike infinity, where the matching condition (1.9) would be automatic. (1.3), (1.9), the Heisenberg evolution operator commutes with both Q±lm and their derivatives, so it depends only on the hatted radiative variables and is instead independent of the soft one. We should point out here that this derivation can be generalized to the case when in- and out- operators do not evolve unitarily but are still related by a linear map This is the case that applies to fields that scatter to I+ in a collapsing black hole geometry.
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