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SUMMARY:From the Origins of Twistor Theory to Bi-Twistors and Curved Space
 -Times - Roger Penrose (University of Oxford)
DTSTART:20240911T143000Z
DTEND:20240911T153000Z
UID:TALK219631@talks.cam.ac.uk
DESCRIPTION:Twistor theory was originated in late 1963 as a geometric appr
 oach to the quantum field theoretic requirement of splitting the positive-
 frequency modes from the negative frequency ones. This was addressed throu
 gh translating the geometry of Minkowski space into the projective geometr
 y CP3\, referred to as the projective twistor space PT\, whose division in
 to two halves PT+ and PT&ndash\; geometrically described the required posi
 tive/negative frequency splitting.\n&nbsp\;\nHowever\, as the geometry of 
 twistor theory progressed\, in relation to its physical interpretation in 
 terms of the momentum/angular momentum of photon states\, it became clear 
 that the splitting of PT into PT+ and PT&ndash\; had more directly to do w
 ith positive/negative helicity than with positive/negative frequency.\n&nb
 sp\;\nThis confusion of interpretation became more manifest with the non-l
 inear graviton construction\, whereby twistor theory broadened its scope t
 o describe curved complex space-times\, where the helicity/frequency tensi
 on manifested itself into the &ldquo\;anti-self-dual&rdquo\; requirement f
 or the curved 4-manifolds that could be directly described by curved twist
 or-space theory\, and twistor theory itself bifurcated into a &ldquo\;posi
 tive-definite&rdquo\; version of more interest to pure mathematicians and 
 th &ldquo\;Lorentzian&rdquo\; (or even &ldquo\;split-signature&rdquo\;) ve
 rsion of more direct interest to physicists.\n&nbsp\;\nThe concept of a bi
 -twistor is introduced here to circumvent this asymmetry and (anti-)self-d
 ual requirement\, by involving both twistors and dual twistors together\, 
 subject to their quantum commutation laws\, this providing a bi-twistor tr
 iple product (and a split-octonion algebra)\, enabling general space-times
  to be described by bi-twistors.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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