2015/01/31 by Claus Gerhardt · 10 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Canonical quantization #Constraint (computer-aided design) #Cosmology #Cosmology and Gravitation Theories #Dark energy #Friedmann equations #Geometric quantization #Geometry #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Symplectic geometry #Wheeler–DeWitt equation #gr-qc #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.4310/atmp.2018.v22.n3.a4
published in Advances in Theoretical and Mathematical Physics 22(3), 709-757 · This paper has been published in ATMP 22 (2018) under the title "The quantization of gravity". The title of the arXiv version, however, will remain unchanged since it had been referred to under the original title in a number of other papers
openalex created_date 2016/06/24 · openalex publication_date 2018/01/01 · arxiv created 2018/10/22 · arxiv updated 2018/10/23 · openalex updated_date 2026/08/05
In a former paper we proposed a model for the quantization of gravity by working in a bundle E where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system. \nd In the second model the resulting equation is a wave equation in \so × (0,∞) valid in points (x,t,ξ) in E and we look for solutions for each fixed ξ. This set of equations contains as a special case the equation of a quantized cosmological Friedmann universe without matter but with a cosmological constant, when we look for solutions which only depend on t. Moreover, in case \so is compact we prove a spectral resolution of the equation.