Abstract Sharply peaked quantum states are conjectured to be conducive to the notion of a quantum-corrected spacetime. We investigate this conjecture for a flat-FLRW model with perfect fluid, where a generalized ordering scheme is considered for the gravitational Hamiltonian. We study the implications of different ordering choices on the dynamics of the quantum Universe. We demonstrate that the imprints of the operator ordering ambiguity are minimal, and quantum fluctuations are small in the case of sharply peaked states, leading to a consistent notion of a quantum-corrected spacetime defined via the expectation value of the scale factor. Surprisingly, the ordering imprints survive far away from the singularity through the quantum fluctuations in the quantum-corrected spacetime for broadly peaked states.

Quantum Mechanics in Curved Configurational Space Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the Rimannian configurational spaces. A unique rule of ordering of operators in the canonical formalism and a unique definition of the path integral are established and, thus, a part of ambiguities in the quantum counterpart of geodesic motion is removed. A geometric interpretation is proposed for non-invariance of the quantum mechanics on coordinate transformations. An approach alternative to the quantization of geodesic motion is surveyed, which starts with the quantum theory of a neutral scalar field. Consequences of this alternative approach and the three formalisms of quantization are compared. In particular, the field theoretical approach generates a deformation of the canonical commutation relations between coordinates and momenta of a prticle. A possible cosmological consequence of the deformation is presented in short.

This is possible because the introduction of a minimum length comes with an ordering ambiguity much like the ordering ambiguity that arises with the introduction of hbar in the process of quantization. Published as: Phys.Rev. D71 (2005) 023503 DOI: 10.1103/PhysRevD.71.023503 arXiv categories: astro-ph gr-qc hep-th

Ordering ambiguity versus representation In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved cases. Published as: Journal of Physics A: Math. Gen., vol. 39, pages 203-208 (2006) DOI: 10.1088/0305-4470/39/1/014 arXiv categories: quant-ph