1994/04/24 by Guillermo A. Mena Marugan, Guillermo A Mena Marugán · 7 citations
Physics and Astronomy · #Basis (linear algebra) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Eigenfunction #Gravitation #Hilbert space #Massless particle #Noncommutative and Quantum Gravity Theories #Quantum state #Scalar (mathematics) #Spacetime #Superposition principle #Wormhole #gr-qc
paper · pdf · doi:10.1088/0264-9381/11/9/006
published in Classical and Quantum Gravity 11(9), 2205-2217 (IOP Publishing) · 23 pages (Latex), Preprint CGPG-94/4-4
arxiv created 1994/04/24 · openalex publication_date 1994/09/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.