TY - JOUR

T1 - A nonlinear quantum model of the Friedmann universe.

AU - Wang, Charles

PY - 2003/6/25

Y1 - 2003/6/25

N2 - 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.

AB - 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.

U2 - 10.1088/0264-9381/20/14/316

DO - 10.1088/0264-9381/20/14/316

M3 - Journal article

VL - 20

SP - 3151

EP - 3164

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 1361-6382

IS - 14

ER -