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The quantization of gravity: The quantization of the full Einstein equations
- Source :
- Symmetry 15, 1599, 2023
- Publication Year :
- 2023
-
Abstract
- We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, 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 $\mathbb{R}_+$. In case $n\ge 17$ and provided the cosmological constant $\Lambda$ is negative the temporal eigenfunctions are eigenfunctions of a self-adjoint operator $\hat H_0$ such that the eigenvalues are countable and the eigenfunctions form an orthonormal basis of a Hilbert space.<br />Comment: Feature Paper https://www.mdpi.com/2073-8994/15/8/1599
- Subjects :
- Physics - General Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Symmetry 15, 1599, 2023
- Publication Type :
- Report
- Accession number :
- edsarx.2308.12974
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3390/sym15081599