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SUMMARY:Energy-parity from a bicomplex algebra - Peter Millington\, Univer
 sity of Nottingham
DTSTART:20180223T160000Z
DTEND:20180223T170000Z
UID:TALK98890@talks.cam.ac.uk
CONTACT:Francesca Chadha-Day
DESCRIPTION:There is a long history of attempts to alleviate the sensitivi
 ty of quantum field theory to vacuum fluctuations and ultraviolet divergen
 ces by introducing states of negative norm or states of negative energy.  
 This history involves early works by Dirac\, Pauli\, Pontrjagin and Krein\
 , as well as more recent suggestions by Linde\, Kaplan and Sundrum\, and '
 t Hooft and Nobbenhuis.  In this talk\, we will attempt to construct viabl
 e scalar quantum field theories that permit positive- and negative-energy 
 states by replacing the field of complex numbers by the commutative ring o
 f bicomplex numbers.  The two idempotent zero divisors of the bicomplex nu
 mbers partition the algebra into two ideal subalgebras\, and we associate 
 one with positive-energy modes and the other with negative-energy modes.  
 In so doing\, we avoid destabilising negative-energy cascades\, while real
 ising a discrete energy-parity symmetry that eliminates the vacuum energy.
   The probabilistic interpretation is preserved by associating expectation
  values with the Euclidean inner product of the bicomplex numbers\, and bo
 th the positive- and negative-energy Fock states have positive-definite Eu
 clidean norms.  We consider whether this construction can yield transition
  probabilities consistent with the usual scattering theory and highlight p
 otential limitations.  We conclude by commenting on the extension to spino
 r\, vector and tensor fields.
LOCATION:CMS\,  Potter Room (B1.19)
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