2009/01/14 by Rubén Cordero, Ruben Cordero, Alberto Molgado +2 · 43 citations
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Canonical quantization #Canonical transformation #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Geometric quantization #Hamiltonian (control theory) #Hamiltonian constraint #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum cosmology #Quantum gravity #Quantum mechanics #Theoretical physics #gr-qc
paper · pdf · doi:10.1103/physrevd.79.024024
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 79(2) (American Physical Society) · 11 pages, 2 figures, accepted for publication in Phys. Rev. D
arxiv created 2009/01/14 · openalex publication_date 2009/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an alternative geometric inspired derivation of the quantum cosmology arising from a brane universe in the context of geodetic gravity. We set up the Regge-Teitelboim model to describe our universe, and we recover its original dynamics by thinking of such field theory as a second-order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. Our analysis highlights the second-order derivative nature of the RT model and the inherited geometrical aspect of the theory. A canonical transformation brings us to the internal physical geometry of the theory and induces its quantization straightforwardly. By using the Dirac canonical quantization method our approach comprises the management of both first- and second-class constraints where the counting of degrees of freedom follows accordingly. At the quantum level our Wheeler-De Witt equation agrees with previous results recently found. On these lines, we also comment upon the compatibility of our approach with the Hamiltonian approach proposed by Davidson and coworkers.