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AuthorShalaby, Abouzeid M.
Available date2016-03-06T14:12:57Z
Publication Date2014-05
Publication NameInternational Journal of Modern Physics A
CitationShalaby, A.M. "Isomorphic hilbert spaces associated with different complex contours of the PT-symmetric (-x^4)theory" (2014) International Journal of Modern Physics A, 29 (11-12), art. no. 1450059
AbstractIn this work, we stress the existence of isomorphisms which map complex contours from the upper half to contours in the lower half of the complex plane. The metric operator is found to depend on the chosen contour but the maps connecting different contours are norm-preserving. To elucidate these features, we parametrized the contour considered in Phys. Rev. D 73, 085002 (2006) for the study of wrong sign x4 theory. For the parametrized contour of the form , we found that there exists an equivalent Hermitian Hamiltonian provided that a2c is taken to be real. The equivalent Hamiltonian is b-independent but the metric operator is found to depend on all the parameters a, b and c. Different values of these parameters generate different metric operators which define different Hilbert spaces. All these Hilbert spaces are isomorphic to each other even for the parameter values that define contours with ends in two adjacent wedges. As an example, we showed that the transition amplitudes associated with the contour are exactly the same as those calculated using the contour , which is not PT-symmetric and has ends in two adjacent wedges in the complex plane.
PublisherWorld Scientific Publishing Co.
SubjectMetric operator
SubjectNon-Hermitian models
SubjectPT -symmetric theories
SubjectStokes wedges
TitleIsomorphic Hilbert spaces associated with different complex contours of the PT-symmetric (-x^4) theory
Issue Number11
Volume Number29

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