BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

We consider scattering of Faddeev-Kulish electrons in QED and study the entanglement between the hard and soft particles in the final state at the perturbative level. The soft photon spectrum naturally splits into two parts: i) soft photons with energies less than a characteristic infrared scale E d present in the clouds accompanying the asymptotic charged particles, and ii) sufficiently low energy photons with energies greater than E d , comprising the soft part of the emitted radiation. We construct the density matrix associated with tracing over the radiative soft photons and calculate the entanglement entropy perturbatively. We find that the entanglement entropy is free of any infrared divergences order by order in perturbation theory. On the other hand infrared divergences in the perturbative expansion for the entanglement entropy appear upon tracing over the entire spectrum of soft photons, including those in the clouds. To leading order the entanglement entropy is set by the square of the Fock basis amplitude for real single soft photon emission, which leads to a logarithmic infrared divergence when integrated over the photon momentum. We argue that the infrared divergences in the entanglement entropy in this latter case persist to all orders in perturbation theory in the infinite volume limit.

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“…The case | q γ | > E d is covered by the previous analysis. Such amplitudes in QED and gravity were recently studied in [35,23].…”

Section: Single Soft Photon Productionmentioning

confidence: 99%

IR dynamics and entanglement entropy

Tomaras

Toumbas

2020

Phys. Rev. D

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“…As was done in [37] for the leading soft dressings, we aim to construct the subleading soft dressed state by using superrotation charge conservation. Since Q S (Y g ) is of the form a − a † , we want to consider a coherent state of the form…”

Section: Subleading Soft Dressingmentioning

confidence: 99%

“…If we treat supertranslation (associated with simple poles) separately as in [37], we may assume that N µν in,out do not possess poles. Then it follows that…”

Section: )mentioning

confidence: 99%

Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity

Choi

Akhoury

2019

J. High Energ. Phys.

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We construct Faddeev-Kulish states in QED and perturbative quantum gravity to subleading order in the soft momentum expansion and to first order in the coupling constant, using the charge conservation formula of asymptotic symmetries associated with the tree-level subleading soft theorems. We demonstrate that the emission and absorption of soft photons/gravitons in dressed amplitudes vanish. The fact that no additional soft radiation may be added to a dressed amplitude supports the claim that, in the dressed state formalism, the soft and hard sectors of scattering processes are correlated. We also show that the dressed virtual amplitudes are equivalent to the infrared-finite part of the traditional amplitudes constructed using Fock states. Since there is no real soft radiation in the asymptotic Hilbert space, the dressed state formalism gives the same cross sections as the Bloch-Nordsieck method.

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“…This subtlety is now well understood for supertranslations. It was shown in [40][41][42][43] that the action of the supertranslation soft charge maps a standard Fock vaccuum to a supertranslated state which can be thought of as being labelled by 9 The authors would like to thank Abhay Ashtekar and Miguel Campiglia for explaining this subtlety to us in detail in the context of supertranslations, and Prahar Mitra for patiently explaining to us why this subtlety cannot be avoided when we look at Ward identities associated with double soft theorems [38,39] …”

Section: E→0mentioning

confidence: 99%

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

Kundu

Ray

2018

Phys. Rev. D

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It is now well understood that Ward identities associated with the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the subleading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated with BMS symmetries in scattering states defined around (non-Fock) vacua parametrized by supertranslations or superrotations.

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BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

Cited by 73 publications

References 27 publications

IR dynamics and entanglement entropy

IR dynamics and entanglement entropy

Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity

Double soft graviton theorems and Bondi-Metzner-Sachs symmetries

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