Mathematics – Logic
Scientific paper
Aug 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988gregr..20..755b&link_type=abstract
General Relativity and Gravitation, Volume 20, Issue 8, pp.755-763
Mathematics
Logic
2
Cosmology:Quantum Gravity, Quantum Gravity:Cosmology
Scientific paper
A Monte Carlo simulation method which yields groundstate wave functions for multielectron atoms is applied to quantized cosmological models. In quantum mechanics, the propagator for the Schrödinger equation reduces to the absolute value squared of the groundstate wave function in the limit of infinite Euclidean time. The wave function of the universe as the solution to the Wheeler-DeWitt equation may be regarded as the zero energy mode of a Schrödinger equation in coordinate time. The simulation evaluates the path integral formulation of the propagator by constructing a large number of paths and computing their contribution to the path integral using the Metropolis algorithm to drive the paths toward a global minimum in the path energy. The result agrees with a solution to the Wheeler-DeWitt equation which has the characteristics of a nodeless groundstate wave function. Oscillatory behavior cannot be reproduced although the simulation results may be physically reasonable. The primary advantage of the simulations is that they may easily be extended to cosmologies with many degrees of freedom. Examples with one, two, and three degrees of freedom (d.f.) are presented.
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