A functional approach to soft graviton scattering and BMS charges

Abstract

We consider the interaction between a matter system and soft gravitons. We use a functional eikonal expansion to deal with the infrared divergences, and introduce a "composite generating functional" which allows us to calculate a decoherence functional for the time evolution of the system. These techniques allow us to formulate scattering problems in a way which deals consistently with infrared effects, as well as being manifestly diffeomorphism invariant. We show how the asymptotic form of the decoherence functional can be written in terms of the infinitely many conserved charges associated with asymptotic BMS symmetries, and allow us to address the question of how much information is lost during the scattering.

Soft theorems from boundary terms in the classical point particle currents

“…We then show how the factorization property generalizes simply to all hard amplitudes in the theory. Some of this has been discussed before by us, using the language of influence functionals [27].…”

“…Consistent approaches to the IR divergences and factorization can also be set up using a systematic eikonal expansion [17,18], which has been employed in recent years to study soft graviton effects in contexts ranging from gravitational decoherence to Hawking radiation [19][20][21][22][23][24][25][26][27]. One can also address these divergences by "dressing" the asymptotic states of the matter particles using coherent boson states [28][29][30][31][32][33][34][35][36][37]; these dressed states can be imagined as a "cloud" of soft gauge bosons surrounding charged particles.…”

“…The question of how soft gauge bosons cause decoherence of matter states can also be related to asymptotic states. In QED, studies of decoherence are quite old [59,60]; more recent work on both soft photon and soft graviton decoherence [27,61,62] indicates that matter states are almost completely decohered over long times except under very special circumstances, although the problem is not completely resolved [63,64]; the connection with asymptotic states can be understood in various ways [27,62]. In this context it is interesting that scattering using dressed states [62] seems to exhibit interference terms which are more in line with what is seen in finite time experiments.…”

UV and IR divergence-free calculation of the vertex function at arbitrary momentum transfer

“…Infrared divergence is a significant problem in many areas of physics, from Yang-Mills theory 3,4 , cosmology 5 and quantum gravity 6 to high energy physics 7 .…”

Gauge Invariant Propagators and States in Quantum Electrodynamics

“…(ii) If one is dealing with state superpositions involving a large spatial separation of charge or mass, real confusion arises in discussion of what are the correct physical variables, or how to test, eg., whether or not the gravitational metric field g µν (x) is quantized [34][35][36]. The related question of how to properly define notions like decoherence is also unclear, with different results being derived for decoherence rates by different authors [33,[37][38][39][40].…”