2019/01/16 by Iñaki Garay, Garay, Iñaki, Salvador Robles-Pérez +1
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1901.05171
openalex publication_date 2019/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A canonical quantisation of the coordinates of the spacetime within the general relativity theory is proposed. This quantisation will depend on the observer but it provides an interesting perspective on the problem of relating the non-relativistic and classical limits of a possible quantum gravity theory. In this sense, within this formalism, it is possible to recover from the quantum equation satisfied by a test field the classical geodesics of the corresponding spacetime. On the other hand, the Schrödinger equation is recovered in the Newtonian limit. A key ingredient for this procedure is a generalization of the Maupertuis principle, that is, the possibility of describing the geodesics of a given metric as the non-affine geodesics of other conformal metric under the action of a potential.