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CATEGORIES:HEP phenomenology joint Cavendish-DAMTP seminar
SUMMARY:Energy-parity from a bicomplex algebra - Peter Mil
lington\, University of Nottingham
DTSTART;TZID=Europe/London:20180223T160000
DTEND;TZID=Europe/London:20180223T170000
UID:TALK98890AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/98890
DESCRIPTION:There is a long history of attempts to alleviate t
he sensitivity of quantum field theory to vacuum f
luctuations and ultraviolet divergences by introdu
cing states of negative norm or states of negative
energy. This history involves early works by Dir
ac\, Pauli\, Pontrjagin and Krein\, as well as mor
e recent suggestions by Linde\, Kaplan and Sundrum
\, and 't Hooft and Nobbenhuis. In this talk\, we
will attempt to construct viable scalar quantum f
ield theories that permit positive- and negative-e
nergy states by replacing the field of complex num
bers by the commutative ring of bicomplex numbers.
The two idempotent zero divisors of the bicomple
x numbers partition the algebra into two ideal sub
algebras\, and we associate one with positive-ener
gy modes and the other with negative-energy modes.
In so doing\, we avoid destabilising negative-en
ergy cascades\, while realising 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 both
the positive- and negative-energy Fock states hav
e positive-definite Euclidean norms. We consider
whether this construction can yield transition pro
babilities consistent with the usual scattering th
eory and highlight potential limitations. We conc
lude by commenting on the extension to spinor\, ve
ctor and tensor fields.
LOCATION:CMS\, Potter Room (B1.19)
CONTACT:Francesca Day
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