A Unified Quantization of Gravity and Other Fundamental Forces of Nature

Abstract

We quantized 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 HSM and the Hamilton function of gravity by HG. Working in a fiber bundle E with base space S0=Rn, where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form HG+HSM=HG+t−23H˜SM, if n=3, where H˜SM depends on metrics σij satisfying detσij=1. In the quantization process, we quantize HG for general σij but H˜SM only for σij=δij by the usual methods of QFT. Let v resp. ψ be the spatial eigendistributions of the respective Hamilton operators, then, the solutions u of the Wheeler–DeWitt equation are given by u=wvψ, where w satisfies an ODE and u is evaluated at (t,δij) in the fibers.