The Brazilian gauge potential Bu^a is the non-trivial part of the dimensionless TETRAD

eu^a = (Kronecker Delta)u^a + Bu^a

that I call

Bu ~ Lp^2(Goldstone Phase),u

Bu = Bu^aLp^2Pa/h

Bu^aPa/h = (Macro-Quantum Vacuum Coherent Goldstone Phase),u

{Pa} is the mom-energy Lie algebra generating the translation Lie group T4


Bu has dimensions of length.


The non-dynamical torsion-free 1916 GR Ricci Rotation coefficients are

A^abu = e^aweb^w;u

where ;u is the {LC} covariant derivative

The Lorentz group is not yet locally gauged in 1916 GR only T4 is locally gauged.

;u = ,u - i/2A^abuSab

Where ,u is ordinary partial derivative and {Sab} is the Lie algebra of the Lorentz Lie group.

Sab = (i/4)[&a,&b]

&a are the 4x4 Dirac gamma matrices that generate the Dirac Clifford Algebra

This GCT {LC} covariant derivative operates on Dirac spinor fields.