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PT-symmetry, indefinite metric, and nonlinear quantum mechanics

Brody, Dorje Corje (2017) PT-symmetry, indefinite metric, and nonlinear quantum mechanics Journal of Physics A: Mathematical and Theoretical, 50 (48). pp. 1-12.

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If a Hamiltonian of a quantum system is symmetric under space-time reflection, then the associated eigenvalues can be real. A conjugation operation for quantum states can then be defined in terms of space-time reflection, but the resulting Hilbert space inner product is not positive definite and gives rise to an interpretational difficulty. One way of resolving this difficulty is to introduce a superselection rule that excludes quantum states having negative norms. It is shown here that a quantum theory arising in this way gives an example of Kibble’s nonlinear quantum mechanics, with the property that the state space has a constant negative curvature. It then follows from the positive curvature theorem that the resulting quantum theory is not physically viable. This conclusion also has implications to other quantum theories obtained from the imposition of analogous superselection rules.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Brody, Dorje
Date : 7 November 2017
DOI : 10.1088/1751-8121/aa91e2
Uncontrolled Keywords : Bergman kernel; Hyperbolic quantum mechanics; PT symmetry; Superselection
Depositing User : Claudio Svaluto
Date Deposited : 11 Oct 2018 09:22
Last Modified : 11 Oct 2018 09:22

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