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SUMMARY:Extension of the CPT Theorem to non-Hermitian Hamiltonians and Uns
table States (15' + 5')
DTSTART;VALUE=DATE-TIME:20160806T150000Z
DTEND;VALUE=DATE-TIME:20160806T152000Z
DTSTAMP;VALUE=DATE-TIME:20200128T103256Z
UID:indico-contribution-1072005@indico.cern.ch
DESCRIPTION:Speakers: Philip Mannheim (University of Connecticut)\nWe exte
nd the CPT theorem to quantum field theories with non-Hermitian Hamiltonia
ns and unstable states. Our derivation is a quite minimal one as it requir
es only the time-independent evolution of scalar products\, invariance und
er complex Lorentz transformations\, and a non-standard but nonetheless pe
rfectly legitimate interpretation of charge conjugation as an antilinear o
perator. The first of these requirements does not force the Hamiltonian to
be Hermitian. Rather\, it forces its eigenvalues to either be real or to
appear in complex conjugate pairs\, forces the eigenvectors of such conjug
ate pairs to be conjugates of each other\, and forces the Hamiltonian to
admit of an antilinear symmetry. The latter two requirements then force th
is antilinear symmetry to be CPT\, while forcing the Hamiltonian to be rea
l rather than Hermitian. Our work justifies the use of the CPT theorem in
establishing the equality of the lifetimes of unstable particles that are
charge conjugates of each other. We show that the Euclidean time path inte
grals of a CPT-symmetric theory must always be real. In the quantum-mechan
ical limit the key results of the PT symmetry program of Bender and collab
orators are recovered\, with the C-operator of the PT symmetry program bei
ng identified with the linear component of the charge conjugation operator
.\n\nhttps://indico.cern.ch/event/432527/contributions/1072005/
LOCATION: Superior A
URL:https://indico.cern.ch/event/432527/contributions/1072005/
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