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# Infrared Problems in QED and Quantum Gravity

COVID-19 information for PI Residents and Visitors

Conference Date:
Mercredi, Décembre 7, 2016 (All day) to Jeudi, Décembre 8, 2016 (All day)
Scientific Areas:
Quantum Gravity

Infrared problems in quantum field theory lead to many surprising phenomena in scattering theory (e.g. polarization of the vacuum, breaking of Lorentz symmetry, delocalization of the charge), due to existence of massless gauge bosons (photons in QED). Although there are well tested algorithms for computing probabilities of experimental scattering processes, the conceptual understanding of the problem is still very poor. There are strong indications that the same, or even worse, conceptual problems would have to be solved in quantum gravity, due to the presence of the massless graviton. Recently, there have been some advances in understanding the infrared problem in QED, coming from different research communities. The aim of this workshop is to bring together key researchers from these communities who work on infrared problems and to give them opportunity to discuss and start new interdisciplinary collaborations.

• Abhay Ashtekar, Pennsylvania State University
• Miguel Campiglia, Universidad de Montevideo
• Maximilian Duell, Technical University of Munich
• Wojciech Dybalski, Technical University of Munich
• Laurent Freidel, Perimeter Institute
• Barak Gabai, Perimeter Institute
• Andrzej Herdegen, Cracow Jagiellonian University
• Sebastian Mizera, Perimeter Institute
• Aldo Riello, Perimeter Institute
• Burkhard Schwab, Harvard University
• Abhay Ashtekar, Pennsylvania State University
• Freddy Cachazo, Perimeter Institute
• Miguel Campiglia, Universidad de Montevideo
• Sylvain Carrozza, Perimeter Institute
• Lin-Qing Chen, Perimeter Institute
• Bianca Dittrich, Perimeter Institute
• Maximilian Duell, Technical University of Munich
• Wojciech Dybalski, Technical University of Munich
• Laurent Freidel, Perimeter Institute
• Barak Gabai, Perimeter Institute
• Marc Geiller, Perimeter Institute
• Henrique Gomes, Perimeter Institute
• Daniel Guariento, Perimeter Institute
• Andrzej Herdegen, Cracow Jagiellonian University
• Sebastian Mizera, Perimeter Institute
• Kasia Rejzner, Perimeter Institute & University of York
• Aldo Riello, Perimeter Institute
• Laura Sberna, Perimeter Institute
• Burkhard Schwab, Harvard University
• Barak Shoshany, Perimeter Institute
• Vasudev Shyam, Perimeter Institute
• Lee Smolin, Perimeter Institute

Wednesday, December 7, 2016

 Time Event Location 8:30 – 9:00am Registration Reception 9:00 – 9:05am Kasia Rejzner, Perimeter Institute & University of YorkWelcome and Opening Remarks Sky Room 9:05 – 10:05am Abhay Asktekar, Pennsylvania State UniversityNull Infinity, BMS Group and Infrared Sectors Sky Room 10:05 – 10:30am Coffee Break Bistro – 1st Floor 10:30 – 11:30am Burkhard Schwab, Harvard UniversityLarge gauge symmetries and black hole absorption rates Sky Room 11:30 – 12:30pm Barak Gabai, Perimeter InstituteLarge Gauge Symmetries and Asymptotic States in QED Sky Room 12:30 – 2:30pm Lunch Bistro – 1st FloorReserved Table 2:30 – 3:30pm Wojciech Dybalski, Technical University of MunichNon-relativistic QED in different gauges Sky Room 3:30 – 4:30pm Andrzej Herdegen, Cracow Jagiellonian UniversityAsymptotic structure of electrodynamics revisited Sky Room 4:30 – 5:00pm Coffee Break Bistro – 1st Floor 5:00pm Open Discussion Sky Room

Thursday, December 8, 2016

 Time Event Location 9:00 – 10:00am Maximilian Duell, Technical University of MunichScattering of atoms and non-locality of the vacuum in QED Sky Room 10:00 – 10:30am Coffee Break Bistro – 1st Floor 10:30 – 11:30am Aldo Riello, Perimeter InstituteTBA Sky Room 11:30 – 12:30pm Miguel Campiglia, Universidad de Montevideo$U(1)$ asymptotic charges and soft photons Sky Room 12:30 – 2:30pm Lunch Bistro – 1st FloorReserved Table 2:30 – 3:30pm Sebastian Mizere, Perimeter InstituteSoft Theorems from Riemann Spheres Sky Room 3:30 – 4:30pm Laurent Freidel, Perimeter InstituteTBA Sky Room 4:30 – 5:00pm Coffee Break Bistro – 1st Floor 5:00pm Open Discussion Sky Room

Null Infinity, BMS Group and Infrared Sectors

I will provide a broad overview of the relation between the structure of null infinity and infrared sectors for the Maxwell theory and full, non-linear general relativity. I hope this talk will serve as an introduction for the talks that will follow.

$U(1)$ asymptotic charges and soft photons

In the first part of the talk I will describe how the subleading soft photon theorem can be understood as a Ward identity of singular $O(r)$ large gauge symmetry at null infinity. In the second part I will present a space-infinity description of the $O(1)$ large gauge symmetry that arise in the context of the leading soft photon theorem.

Maximilian Duell, Technical University of Munich

Scattering of atoms and non-locality of the vacuum in QED

In the setting of algebraic QFT we give a mathematically rigorous construction of the scattering matrix for massive Wigner particles in the presence of massless excitations. Our analysis may be applied, in particular, to the scattering of electrically neutral particles in QED. In contrast to previous approaches we do not impose any technical assumptions on the spectrum of the mass operator near the particle masses. Instead, our approach relies on non-local features of the relativistic vacuum state which are similar to the well established Reeh-Schlieder property.

Wojciech Dybalski, Technical University of Mun

Non-relativistic QED in different gauges

Charges localized at spacelike infinity are a traditional ingredient of discussions of the infrared  problems in QED in mathematical physics. It is an old  conjecture that these charges depend on the gauge fixing in the quantization procedure. In this talk I will discuss  this problem in a non-relativistic model of QED. I will  show how to pass from the usual Coulomb gauge to the axial gauge,  compute the charges in both cases and give arguments in favour  of the above conjecture. Rigorous mathematical conclusions are  hindered (so far) by severe infrared problems in the axial gauge.

Barak Gabai, Perimeter Institute

Large Gauge Symmetries and Asymptotic States in QED

Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.

Andrzej Herdegen, Cracow Jagiellonian University

Asymptotic structure of electrodynamics revisited

The lecture presents a personal view on the asymptotic structure of electrodynamics. Asymptotic variables form an algebra, in which infrared–long-range degrees of freedom count among full-fledged observables, not merely superselection labels.

Sebastian Mizere, Perimeter Institute

Soft Theorems from Riemann Spheres

I will review the reformulation of the S-matrix in terms of Riemann spheres due to Cachazo, He, and Yuan. I will show how it sheds new light on the derivation of Weinberg soft theorems for General Relativity and Yang-Mills theory, as well as allows to study soft behaviour of other quantum field theories.

Burkhard Schwab, Harvard University

Large gauge symmetries and black hole absorption rates

I will introduce Noether's second theorem as a way to derive the conserved currents associated with asymptotic symmetries. The large gauge symmetries of electromagnetism (along with conservation of energy) fully constrain the absorption rate of low-energy electromagnetic radiation by black holes. I will show this explicitly for non-evaporating, spherically symmetric black holes in arbitrary space-time dimensions larger than 3.

Scientific Organizers:

• Laurent Freidel, Perimeter Institute
• Henrique Gomes, Perimeter Institute
• Kasia Rejzner, Perimeter Institute & University of York