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A nonlinear quantum model of the Friedmann universe

Charles Wang
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Abstract

A discussion is given of the quantisation 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 quantisation scheme that yields a Schrodinger-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 quantisation of a Friedmann Universe with a massive scalar field whose dynamical behaviour is investigated numerically.

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Charles Wang. 2003-07-04. A nonlinear quantum model of the Friedmann universe. https://doi.org/10.1088/0264-9381%2F20%2F14%2F316

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