Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -