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Infrared quantum information

University of British Columbia

Scattering amplitudes in massless gauge field theories have long been known to give rise to infrared divergent effects from the emission of very low energy gauge bosons. The traditional way of dealing with those divergences has been to abandon the idea of measuring amplitudes by only focusing on inclusive cross-sections constructed out of physically equivalent states. An alternative option, found to be consistent with the S-matrix framework, suggested to dress asymptotic states of charged particles by shockwaves of low energy bosons. In this formalism, the clouds of soft bosons, when tuned appropriately, cancel the usual infrared divergences occurring in the standard approach. Recently, the dressing approach has received renewed attention for its connection with newly discovered asymptotic symmetries of massless gauge theories and its potential role in the black hole information paradox. We start by investigating quantum information properties of scattering theory while having only access to a subset of the outgoing state. We give an exact formula for the von Neuman entanglement entropy of an apparatus particle scattered off a set of system particles and show how to obtain late-time expectation values of apparatus observables. We then specify to the case of quantum electrodynamics (QED) and gravity where the unobserved system particles are low energy photons and gravitons. Using the standard inclusive cross-section formalism, we demonstrate that those soft bosons decohere nearly all momentum superpositions of hard particles. Repeating a similar computation using the dressing formalism, we obtain an analogous result: In either framework, outgoing hard momentum states at late times are fully decohered from not having access to the soft bosons. Finally, we make the connection between our results and the framework of asymptotic symmetries of QED and gravity. We give new evidence for the use of the dressed formalism by exhibiting an inconsistency in the scattering of wavepackets in the original inclusive cross-section framework.

Text

2018-08-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/66714

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/