The quantization of gravity: Quantization of the Hamilton equations

Abstract

We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\ne 4$. 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 $SL(n,\mathbb{R}[])/SO(n)$. Since one can define a Schwartz space and tempered distributions in $SL(n,\mathbb{R}[])/SO(n)$ 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.

33 pages, v2: Typos corrected and two sections added. This is the published version

Cited by in corpus (2)

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