PT-Symmetric Quantum Theory Defined in a Krein Space

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dc.creatorTanaka, Toshiaki
dc.date2006-03-13
dc.date2006-05-17
dc.date.accessioned2026-07-07T10:46:11Z
dc.date.available2026-07-07T10:46:11Z
dc.descriptionWe provide a mathematical framework for PT-symmetric quantum theory, which is applicable irrespective of whether a system is defined on R or a complex contour, whether PT symmetry is unbroken, and so on. The linear space in which PT-symmetric quantum theory is naturally defined is a Krein space constructed by introducing an indefinite metric into a Hilbert space composed of square integrable complex functions in a complex contour. We show that in this Krein space every PT-symmetric operator is P-Hermitian if and only if it has transposition symmetry as well, from which the characteristic properties of the PT-symmetric Hamiltonians found in the literature follow. Some possible ways to construct physical theories are discussed within the restriction to the class K(H).
dc.description8 pages, no figures; Refs. added, minor revision
dc.identifierhttps://arxiv.org/abs/hep-th/0603096
dc.identifierhttp://arxiv.org/abs/hep-th/0603096
dc.identifierJ.Phys.A39:L369,2006
dc.identifierdoi:10.1088/0305-4470/39/22/L04
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183151
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectFunctional Analysis
dc.subjectQuantum Physics
dc.titlePT-Symmetric Quantum Theory Defined in a Krein Space
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