Persistence Amplitudes from Numerical Quantum Gravity

Details Persistence Amplitudes from Numerical Quantum Gravity Persistence Amplitudes from Numerical Quantum Gravity

1997-12-09

arxiv.org/abs/gr-qc/9712043v1

Class.Quant.Grav. 15 (1998) 3435-3447

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 12 figures (bitmapped postscript), a postscript version of this paper with high quality postscript figures may be fo

Scientific paper

10.1088/0264-9381/15/11/010

The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude exp(-I_{classical}/\hbar), where I_{classical} is the Euclidean action of the classical solution joining the initial and final data. In certain cases the tree amplitude is exact. We study I_{classical} hence the quantum amplitude, in the case of a spherically symmetric Riemannian gravitational field coupled to a spherically symmetric scalar field. The classical scalar field obeys an elliptic equation, which we solve using relaxation techniques, in conjunction with the field equations giving the gravitational field. An example of the transition from linearity to non-linearity is presented and power law behavior of the action is demonstrated.

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