Gell-Mann matrices (strong force interaction) in geometric algebra Cl3,0

In this paper, we will find a way to apply the Gell-Mann transformations made by the λi matrices using Geometric Algebra Cl_3,0. And without the need of adding the time as an ad-hoc dimension, but just considering that:

The transformations are as follows. Considering the original ψ:

The new ψ’ obtained when applying each of the Gell-Mann matrices λ_i is:

Considering that Gell-Mann matrices do not consider at all the existence I if and , it is possible that we should consider them zero form the beginning. Anyhow, above relations would correspond with the most general case.

We have also worked in the bra-ket product using geometric algebra. For the Euclidean case we have the equation (where the cross sign means reverse and the asterisk means conjugate, both mean the same in Cl_3,0:

Being ρ the probability density:

And the fermionic current:

We have made the same in the case of orthogonal buy not orthonormal metric, leading to:

But in this case:

And:

It has been also shown that the g-2 issue of the muon could be related to gravitational (non-Euclidean metric) issues without needing another natural force.

The difference of the values of g-2 of the muon are:

And the effect of the non-Euclidean metric on the surface of Earth is: