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Inequivalence of unitarity and self-adjointness: An example in quantum cosmology
Phys. Rev. D 41, 1358 – Published 15 February, 1990
DOI: https://doi.org/10.1103/PhysRevD.41.1358
Abstract
An example of a quantum cosmological model is presented whose dynamics is unitary although the time-dependent Hamiltonian operator fails to be self-adjoint (because it is not defined) for a particular value of t. The model is shown to be singular, and this disproves a conjecture put forward by Gotay and Demaret to the effect that unitary quantum dynamics in a ‘‘slow-time’’ gauge is always nonsingular.
References (7)
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- This is ensured by the spectral theorem. See Methods of Modern Mathematical Physics (Ref. 1), Sec. VIII.6, pp. 263 and 264; F. Riesz and B. Sz.-Nagy, Functional Analysis (Frederick Ungar, New York, 1955), Chap. IX, Sec. 128.