The quantization of gravity

• Verfasst von: Gerhardt, Claus [VerfasserIn]
• Titel: The quantization of gravity
• Titelzusatz: quantization of the Hamilton equations
• Verf.angabe: Claus Gerhardt
• E-Jahr: 2021
• Jahr: 7 April 2021
• Umfang: 28 S.
• Teil: volume:7
• Teil: year:2021
• Teil: number:4
• Teil: elocationid:91
• Teil: extent:28
• Fussnoten: Gesehen am 08.02.2021
• Titel Quelle: Enthalten in: Universe
• Ort Quelle: Basel : MDPI, 2015
• Jahr Quelle: 2021
• Band/Heft Quelle: 7(2021), 4, Artikel-ID 91
• ISSN Quelle: 2218-1997
• DOI: doi:10.3390/universe7040091
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Fourier quantization
• Sach-SW: quantization of gravity
• Sach-SW: quantization of the Hamilton equations
• Sach-SW: quantum gravity
• Sach-SW: symmetric spaces
• Sach-SW: temporal and spatial eigenfunctions
• K10plus-PPN: 1755326238

Abstract

We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form −Δu=0 in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided n≠4. Using then separation of variables, the solutions u can be expressed as products of temporal and spatial eigenfunctions, where the spatial eigenfunctions are eigenfunctions of the Laplacian in the symmetric space SL(n,R)/SO(n). Since one can define a Schwartz space and tempered distributions in SL(n,R)/SO(n) as well as a Fourier transform, Fourier quantization can be applied such that the spatial eigenfunctions are transformed to Dirac measures and the spatial Laplacian to a multiplication operator.