The quantization of gravity: quantization of the Hamilton equations

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...

Full description

Saved in:
Bibliographic Details
Main Author: Gerhardt, Claus (Author)
Format: Article (Journal)
Language:English
Published: 7 April 2021
In: Universe
Year: 2021, Volume: 7, Issue: 4
ISSN:2218-1997
DOI:10.3390/universe7040091
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3390/universe7040091
Verlag, lizenzpflichtig, Volltext: https://www.mdpi.com/2218-1997/7/4/91
Get full text
Author Notes:Claus Gerhardt
Description
Summary: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.
Item Description:Gesehen am 08.02.2021
Physical Description:Online Resource
ISSN:2218-1997
DOI:10.3390/universe7040091