Quantum gravity by relativization of Quantum Field Theory.
Abstract
The question is how can we make quantum field theory part of General
Relativity instead of how we can quantize gravity. Here it will be shown
that a Hilbert space can be defined such that the bra-ket is a four
vector in ℳ\mathcal{M}inkowski space-time,
=va∈ℳ\langle\psi|\phi\rangle=v^{a}\in\mathcal{M}.
Similar to a Hilbert space over the field of quarternions. Minkowski
space is the tangent space at an arbitrary point on a Riemannian
manifold. It will then be shown that the Riemann curvature connects
these spaces by operating on the probability density 4-current
jaj^{a} of the local QFT. Choosing the Klein-Gordon field as a
simple example QFT, the quantized Einstein-Hilbert action will then be
derived. From there the expected Feynman diagrams for General Relativity
can be read off. In this way one may calculate the gravitational effect
due to a quantum field theoretical event.