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SUMMARY:Solving the Scattering Equations - Peter Goddard (Institute for Ad
 vanced Study\, Princeton)
DTSTART:20160630T133000Z
DTEND:20160630T143000Z
UID:TALK66614@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Describing work in collaboration with Louise Dolan\, I will di
 scuss the scattering equations\, originally introduced in 1972 by&nbsp\;Fa
 irlie and Roberts searching for new dual models\,&nbsp\;rediscovered by Gr
 oss&nbsp\;and Mende in 1988\, discussing the high energy&nbsp\;behaviour o
 f string theory\, and more recently shown by&nbsp\;Cachazo\, He and Yuan t
 o provide a kinematic basis for describing&nbsp\;remarkable formulae for t
 ree&nbsp\;amplitudes for massless particles in arbitrary space-time&nbsp\;
 dimension (including scalars\, gauge&nbsp\;bosons and gravitons). We refor
 mulate the scattering equations for&nbsp\;N&nbsp\;particles as a&nbsp\;sys
 tem of N -3 homogeneous polynomial&nbsp\;equations in N - 2 complex variab
 les\, which are linear in each variable separately.&nbsp\;The linearity of
  the equations enables their&nbsp\;explicit solution in terms of the roots
  of a single-variable polynomial of degree&nbsp\;(N-3)!\, which can itself
  be explicitly&nbsp\;constructed in terms of the Mandelstam variables form
 ed from the momenta. The&nbsp\;possible extension to one loop and the&nbsp
 \;special case of four-dimensional space-time may also be briefly discusse
 d.
LOCATION:Seminar Room 1\, Newton Institute
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