## A Gravity, U(4) x U(4) Yang-Mills and Matter Unification in Clifford Spaces

**Authors:** Carlos Castro

A brief review of a Conformal Gravity and U(4) x U(4) Yang-Mills Unification
model in four dimensions from a Clifford Gauge Field Theory in C-spaces
(Clifford spaces) is presented. It based on the (complex) Clifford Cl(4,C) algebra
underlying a complexified four dimensional spacetime (8 real dimensions).
The 16 fermions of each generation can be arranged into the 16 entries of a
4 x 4 matrix associated with the A = 1, 2, 3, ....., 16 indices corresponding to
the dimensions of the Cl(4) gauge algebra. The Higgs sector is also part of
the Cl(4)-algebra polyvector valued gauge field in C-space. The Yukawa couplings
which furnish masses to the fermions (after symmetry breaking) admit a
C-space geometric interpretation as well.

**Comments:** 11 Pages. This article will appear in the special issue of the Invertis Journal of Science and Technology, New Dehli, 2010

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### Submission history

[v1] 18 Dec 2009

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