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Real Tunneling Solutions and the Hartle-Hawking Wave Function

S. Carlip
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Abstract

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing ``momentum'') at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely; consequently, such an instanton will contribute to the wave function at only one or a few isolated spatial geometries. I show that these geometries are the extrema of the Hartle-Hawking wave function in the semiclassical approximation, and provide some evidence that with a suitable choice of time parameter, these extrema are the maxima of the wave function at a fixed time.

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S. Carlip. 1993-01-08. Real Tunneling Solutions and the Hartle-Hawking Wave Function. https://doi.org/10.1088/0264-9381%2F10%2F6%2F004

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