## Structure of the Dirac Equation in ECE Theory

**Feed:** Dr. Myron Evans

**Posted on:** Monday, January 17, 2011 1:06 AM

**Author:** metric345

**Subject:** Structure of the Dirac Equation in ECE Theory

The structure of the Dirac equation of the general spacetime in ECE theory is given directly from Cartan geometry in papers such as UFT 4, 129 and 130. The eigenfunction psi is a tetrad with four components in SU(2) representation space. So from the tetrad postulate the Dirac equation in second order format is obtained as a fermion wave equation:
(d’alembertian + R) psi = 0 This can also be interpreted as a Proca equation for the boson, or the Klein Gordon equation for the spinless particle, and also as a Majorana equation. The usual Dirac equation is obtained by rearranging the 2 x 2 psi in to a 1 x 4 psi and factorizing the d’alembertian with Dirac matrices. Finally take the limit of R = (mc / h bar) squared to obtain the original Dirac equation. The ECE fermion equation of UFT 129 and 130 shows that the fermion equation can be written as a first order equation with a 2 x 2 psi (see also notes for UFT 171 and the forthcoming UFT 172). The 2 x 2 psi is obtained from the definition of the tetrad as a matrix linking 2 spinors (column 2 vectors) in two different representations: 1) R and L; 2) 1 and 2. Similarly the tetrad for electromagnetism is defined as the 4 x 4 matrix linking two four vectors, one in (0), (1), (2), (3) rep, the other on 0, 1, 2, 3 rep. Similarly we can define the tetrad in any SU(n) rep space, or any rep space. This gives a generally covariant unified field theory based on geometry and the philosophy of relativity. The tetrad in ECE is more broadly defined than in the original work of Cartan, which used a tangent Minkowski spacetime labelled a at point P to a base manifold labelled mu. |