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...
Saved in:
| Main 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 
|
| Author Notes: | Claus Gerhardt |
| 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 |