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Title: PT-symmetry, indefinite metric, and nonlinear quantum mechanics
Authors: Brody, DC
Issue Date: 2017
Publisher: IOP publishing
Citation: Journal of Physics A: Mathematical and Theoretical, 2017
Abstract: 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.
ISSN: 1751-8113
Appears in Collections:Dept of Mathematics Embargoed Research Papers

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