Publication: Quantum state of wormholes and path integral
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1991-08-15
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Amer Physical Soc
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Abstract
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface S which divides the spacetime manifold into two disconnected parts. The ground-state wave function is picked out by requiring that there be no matter excitations in the asymptotic region. Once the path integrals over the lapse and shift functions are evaluated, the requirement that the spacetime be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is claimed that no wave function exists which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. The wormhole wave functions are worked out in minisuperspace models with massless minimal and conformal scalar fields.
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© 1991 The American Physical Society.
I am very grateful to Pedro Gonzalez-Diaz for many enlightening discussions and encouraging comments. Also, I wish to thank Guillermo Mena Marugan for valuable explanations and Jonathan Halliwell for useful conversations and for introducing me to some references relevant to this work.
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