Publication: Hilbert space of wormholes
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1993-08-15
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Amer Physical Soc
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Abstract
Wormhole boundary conditions for the Wheeler-DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert-space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler-DeWitt operator is essentially self-adjoint. This provides us with a kind of probabilistic interpretation. In particular, giant wormholes will give extremely small contributions to any wormhole state. We also study the whole spectrum of the Wheeler-DeWitt operator and its role in the calculation of Green's functions and effective low-energy interactions.
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© 1993 The American Physical Society.
I wish to thank Pedro Gonzalez-Diaz, Guillermo Mena Marugan and Peter Tinyakov for their valuable comments on the manuscript. I also thank Instituto de Matematicas y Fisica Fundamental, C.S.I.C., for hospitality. This work was supported by DGICYT under Contract No. PB91-0052 and by a Basque Country Grant. The ESA IUE Observatory is affiliated with the Astrophysics Division, Space Science Department, ESTEC
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