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A nonlinear quantum model of the Friedmann universe.

Research output: Contribution to journalJournal articlepeer-review

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  • Charles Wang
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<mark>Journal publication date</mark>25/06/2003
<mark>Journal</mark>Classical and Quantum Gravity
Issue number14
Volume20
Number of pages14
Pages (from-to)3151-3164
Publication StatusPublished
<mark>Original language</mark>English

Abstract

A discussion is given of the quantization of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantization scheme that yields a Schrödinger-type equation which is in general nonlinear in evolution. Nevertheless, it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantization of a Friedmann universe with a massive scalar field whose dynamical behaviour is investigated numerically.