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SUMMARY:Robert Wald (University of Chicago)
DTSTART:20220407T133000Z
DTEND:20220407T143000Z
DTSTAMP:20260423T023044Z
UID:jomarec/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/jomarec/16/"
 >The memory effect and infrared divergences</a>\nby Robert Wald (Universit
 y of Chicago) as part of JoMaReC - Joint Online Mathematical Relativity Co
 lloquium\n\n\nAbstract\nThe “memory effect” is the permanent relative 
 displacement of test particles after the passage of gravitational radiatio
 n. It is associated with both the propagation of massive bodies out to tim
 elike infinity (“ordinary memory”) or the propagation of radiation out
  to null infinity (“null memory”). The memory effect can be characteri
 zed by the failure of the shear tensor at order 1/r to return to zero at l
 ate times\, even though it is “pure gauge.” Closely analogous effects 
 occur in electromagnetism\, where the vector potential at order 1/r fails 
 to return to zero even though it is “pure gauge.” In both cases\, the 
 Fourier transform of the radiative field has divergent behavior at low fre
 quencies. This gives rise to infrared divergences (i.e.\, infinite numbers
  of “soft” gravitons/photons) in the quantum field theory description 
 if one attempts to describe these states as vectors in the usual Fock Hilb
 ert space representation. To obtain a mathematically sensible quantum scat
 tering theory\, one must allow states with nonvanishing memory in the “i
 n” and “out” Hilbert spaces. An elegant solution to this problem in 
 massive quantum electrodynamics was given by Kulish and Fadeev\, who const
 ructed a Hilbert space of incoming/outgoing charged particle states that a
 re “dressed” with radiative fields of corresponding memory\, so as to 
 yield vanishing large gauge charges at spatial infinity. However\, we show
  that this type of construction fails in quantum gravity. The primary unde
 rlying reason is that the “dressing” contributes to null memory\, ther
 eby invalidating the construction of eigenstates of large gauge charges. I
 n quantum gravity\, there does not appear to be any choice of (separable) 
 Hilbert space of incoming/outgoing states that can accommodate all scatter
 ing states. Thus\, we argue that scattering should be described at the lev
 el of algebraic incoming/outgoing states rather than attempting to artific
 ially restrict states to a particular Hilbert space.\n
LOCATION:https://researchseminars.org/talk/jomarec/16/
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