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...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
7 April 2021
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| In: |
Universe
Year: 2021, Jahrgang: 7, Heft: 4 |
| ISSN: | 2218-1997 |
| DOI: | 10.3390/universe7040091 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3390/universe7040091 Verlag, lizenzpflichtig, Volltext: https://www.mdpi.com/2218-1997/7/4/91 
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| Verfasserangaben: | Claus Gerhardt |
MARC
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| 520 | |a 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. | ||
| 650 | 4 | |a Fourier quantization | |
| 650 | 4 | |a quantization of gravity | |
| 650 | 4 | |a quantization of the Hamilton equations | |
| 650 | 4 | |a quantum gravity | |
| 650 | 4 | |a symmetric spaces | |
| 650 | 4 | |a temporal and spatial eigenfunctions | |
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