**Authors:** Golden Gadzirayi Nyambuya

The Gravitational, Electromagnetic, Weak & the Strong force are here
brought together under a single roof via an extension of Reimann geometry to a new
geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both
the length and the angle of a vector under parallel transport. The affine connection of this
new geometry - the Reimann-Hilbert Space, is a tensor and this leads us to a geodesic
law that truly upholds the Principle of Relativity. The geodesic law emerging from the
General Theory of Relativity (GTR) is well known to be in contempt of the Principle of
Relativity which is a principle upon which the GTR is founded. The geodesic law for
particles in the GTR must be formulated in special (or privileged) coordinate systems i.e.
gaussian coordinate systems whereas the Principle of Relativity clearly forbids the existence
of special (or privileged) coordinate systems in manner redolent of the way the Special
Theory of Relativity forbids the existence of an absolute (or privileged) frame of reference.
In the low energy regime and low spacetime curvature the unified field equations derived
herein are seen to reduce to the well known Maxwell-Procca equation, the none-abelian
nuclear force field equations, the Lorentz equation of motion for charged particles and the
Dirac Equation. Further, to the already existing four known forces, the theory predicts the
existence of yet another force. We have coined this the super-force and this force obeys
SU(4, 4) gauge invariance. Furthermore, unlike in the GTR, gravitation is here represented
by a single scaler potential, and electromagnetic field and the nuclear forces are described
by the electromagnetic vector potential (A_{μ}) which describes the metric tensor i.e. g_{μν} = A_{μ}A_{ν}.
From this (g_{μν} = A_{μ}A_{ν}), it is seen that gravity waves may not exist in the sense envisaged by
the GTR.

**Comments:** 27 pages, first published in the October 2007 Issue of the Aperion Journal. Further work on these ideas is underway.

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[v1] 9 Nov 2009

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