Wave Function of the Universe and Its Meaning

Abstract

For a FRW-spacetime coupled to an arbitrary real scalar field, we endow the solution space of the associated Wheeler-DeWitt equation with a Hilbert-space structure, construct the observables, and introduce the physical wave functions of the universe that admit a genuine probabilistic interpretation. We also discuss a proposal for the formulation of the dynamics. The approach to quantum cosmology outlined in this article is based on the results obtained within the theory of pseudo-Hermitian operators.

9 pages, contributed to the First International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, held in Prag June 2003

References in corpus (3)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology

Cited by in corpus (8)

• Time-dependent version of cryptohermitian quantum theory
• Scattering theory using smeared non-Hermitian potentials
• Solvability and PT-symmetry in a double-well model with point interactions
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• Experiments in PT-symmetric quantum mechanics
• CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model