A Unified Quantization of Gravity and Other Fundamental Forces of Nature

We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Let us abbreviate the spatial Hamilton functions of the Standard Model by \(\textit{H}_\textit{SM}\) and the Hamilton function of gravity by \(\textit{H}_\textit{G}\) . Working in a fiber bundle \(\textit{E}\) with base space \(\textit{S}_{0} = \mathbb {R}^n\) , where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form \(\textit{H}_\textit{G}+\textit{H}_\textit{SM} = \textit{H}_\textit{G}+\textit{t}-\frac{2}{3} \tilde{H}_\textit{SM}\) if \(\textit{n} = 3\) , where \(\tilde{H}_\textit{SM}\) depends on metrics \({\sigma }_{ij}\) satisfying det \({\sigma }_{ij} =1 \) . In the quantization process, we quantize \(\textit{H}_\textit{G}\) for general \({\sigma }_{ij}\) but \(\tilde{H}_\textit{SM}\) only for \({\sigma }_{ij} = {\delta }_{ij}\) by the usual methods of QFT. Let \(\upsilon \) resp. \(\psi \) be the spatial eigendistributions of the respective Hamilton operators, then, the solutions \(\textit{u}\) of the Wheeler-DeWitt equation are given by \(\textit{u} = w{\upsilon }{\psi }\) , where \(w\) satisfies an ODE and \(\textit{u}\) is evaluated at ( \(\textit{t}, {\delta }_{ij}\) ) in the fibers.