Bases of Wormholes in Quantum Cosmology

Abstract

We show that if the space of physical states spanned by the wormhole wave functions can be equipped with a Hilbert structure, such a Hilbert space must coincide with that of the Lorentzian gravitational system under consideration. The physical inner product can then be determined by imposing a set of Lorentzian reality conditions. The Hilbert space of the gravitational model admits in this case a basis of wormhole solutions, and every proper quantum state can be interpreted as a superposition of wormholes. We also argue that the wave functions that form the basis of wormholes must be eigenfunctions of a complete set of compatible observables. The associated eigenvalues provide a set of well-defined wormhole parameters, in the sense that they can be employed to designate the different elements of the basis of wormholes. We analyse in detail the case of a Friedmann-Robertson-Walker spacetime minimally coupled to a massless scalar field. For this minisuperspace, we prove the validity of all the above statements and discuss various admissible choices of bases of wormhole wave functions.

23 pages (Latex), Preprint CGPG-94/4-4

References in corpus (4)

• Minisuperspaces: Observables and Quantization
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Hilbert space of wormholes
• Reality Conditions in Nonperturbative Quantum Cosmology

Cited by in corpus (6)

• Asymptotically anti-de Sitter wormholes
• Is there a problem with quantum wormhole states in N=1 Supergravity?
• The Case of the Missing Wormhole State
• CANONICAL QUANTIZATION OF CYLINDRICALLY SYMMETRIC MODELS
• Involutions on the Algebra of Physical Observables From Reality Conditions
• Euclidean quantum wormholes