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SUMMARY:Scattering from production in 2d
DTSTART;VALUE=DATE-TIME:20210125T123000Z
DTEND;VALUE=DATE-TIME:20210125T143000Z
DTSTAMP;VALUE=DATE-TIME:20210301T082525Z
UID:indico-event-998903@indico.cern.ch
DESCRIPTION:Abstract\n\nIn 1968\, Atkinson proved the existence of functio
ns that satisfy all S-matrix axioms in four spacetime dimensions. His proo
f is constructive and to our knowledge it is the only result of this type.
Remarkably\, the methods to construct such functions used in the proof we
re never implemented in practice. In the present paper\, we test the appli
cability of those methods in the simpler setting of two-dimensional S-matr
ices. We solve the problem of reconstructing the scattering amplitude star
ting from a given particle production probability. We do this by implement
ing two numerical iterative schemes (fixed-point iteration and Newton's me
thod)\, which\, by iterating unitarity and dispersion relations\, converge
to solutions to the S-matrix axioms. We characterize the region in the am
plitude-space in which our algorithms converge\, and discover a fractal st
ructure connected to the so-called CDD ambiguities which we call "CDD frac
tal". To our surprise\, the question of convergence naturally connects to
the recent study of the coupling maximization in the two-dimensional S-mat
rix bootstrap. The methods exposed here pave the way for applications to h
igher dimensions\, and expose some of the potential challenges that will h
ave to be overcome.\n\n\nBased on\n\n2101.05211\n\n\nVideo conference link
\n\nSince we do not need the video conference system of the lecture hall f
or the time being\, we switch back to Zoom.\n\nhttps://indico.cern.ch/even
t/998903/
LOCATION:CERN 4/3-006 - TH Conference Room
URL:https://indico.cern.ch/event/998903/
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