The quantization of gravity: the quantization of the full Einstein equations
We quantized the full Einstein equations in a globally hyperbolic spacetime N=Nn+1, n≥3, and found solutions of the resulting hyperbolic equation in a fiber bundle E which can be expressed as a product of spatial eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial eigenfunct...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 August 2023
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| In: |
Symmetry
Year: 2023, Volume: 15, Issue: 8, Pages: 1-34 |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym15081599 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3390/sym15081599 Verlag, lizenzpflichtig, Volltext: https://www.mdpi.com/2073-8994/15/8/1599 
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| Author Notes: | Claus Gerhardt |
| Summary: | We quantized the full Einstein equations in a globally hyperbolic spacetime N=Nn+1, n≥3, and found solutions of the resulting hyperbolic equation in a fiber bundle E which can be expressed as a product of spatial eigenfunctions (eigendistributions) and temporal eigenfunctions. The spatial eigenfunctions form a basis in an appropriate Hilbert space while the temporal eigenfunctions are solutions to a second-order ordinary differential equation in R+. In case n≥17 and provided the cosmological constant Λ is negative, the temporal eigenfunctions are eigenfunctions of a self-adjoint operator H^0 such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space. |
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| Item Description: | Gesehen am 22.08.2023 |
| Physical Description: | Online Resource |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym15081599 |