Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction of matter fields in terms of which the theory is deparametrized. The resulting theories have true Hamiltonians for their evolution that usually involve square roots, and this poses certain challenges for their implementation as self-adjoint quantum operators. We show in the context of a simple model of a totally constrained theory that one can introduce related, well-defined operators that reproduce semiclassically the same physics as the original ones, at least for states peaked in the regions of phase space where their associated classical quantities are well-defined. © 2012 American Physical Society.
Publication Source (Journal or Book title)
Physical Review D - Particles, Fields, Gravitation and Cosmology
Gambini, R., & Pullin, J. (2012). Self-adjointness in the Hamiltonians of deparametrized totally constrained theories: A model. Physical Review D - Particles, Fields, Gravitation and Cosmology, 86 (6) https://doi.org/10.1103/PhysRevD.86.067501