Quantum cosmological intertwining: Factor ordering and boundary conditions from hidden symmetries

Abstract

We explore the implications of hidden symmetries present in a particular quantum cosmological setting, extending the results reported in \cite{10,11}. In more detail, our case study is constituted by a spatially closed Friedmann-Lema\^ıtre-Robertson-Walker universe, in the presence of a conformally coupled scalar field. The $su(1,1)$ hidden symmetries of this model, together with the Hamiltonian constraint, lead to the gauge invariance of its corresponding Bargmann indices. We subsequently show that some factor-ordering choices can be related to the allowed spectrum of Bargmann indices and hence, to the hidden symmetries. Moreover, the presence of those hidden symmetries also implies a set of appropriate boundary conditions to choose from. In summary, our results suggest that factor ordering and boundary conditions can be intertwined when a quantum cosmological model has hidden symmetries.

13 pages, no figure, to appear in Phys. Rev. D

References in corpus (10)

• An effective approach to the problem of time
• Change in Hamiltonian General Relativity from the Lack of a Time-like Killing Vector Field
• Does Current Data Prefer a Non-minimally Coupled Inflaton?
• Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology
• Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid
• Signature change from Schutz's canonical quantum cosmology and its classical analogue
• Schrödinger-Wheeler-DeWitt equation in chaplygin gas FRW cosmological model
• Dirac observables and boundary proposals in quantum cosmology
• Factor ordering and large-volume dynamics in quantum cosmology
• On the relation between boundary proposals and hidden symmetries of the extended pre-big bang quantum cosmology

Cited by in corpus (10)

• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Classical Universe emerging from quantum cosmology without horizon and flatness problems
• Shape Invariant Potentials in Supersymmetric Quantum Cosmology
• Experimental investigation of uncertainty relations for non-Hermitian operators
• Summing over Non-singular Paths in Quantum Cosmology
• Operator Ordering Ambiguity and Third Quantization
• Classical Universe Arising from Quantum Cosmology
• Imprints of the operator ordering ambiguity on the dynamics of perfect fluid dominated quantum universe
• Quantum Cosmology in $f(R,T)$ Theory with Schutz's Perfect Fluid