Hello Geoffrey
Thanks for your essay. Please excuse me for putting a spanner in the works, but it does not seem to depict the original theory with the most appropriate maths. This has a substantial bearing on interpretation and future progress.
The point at issue is the algebra underlying Dirac's equation. At each point, this is the Clifford algebra of the metric on space-time. You write that it is "similar to Clifford algebra (complex quaternions)". This statement is unfortunately true - unfortunately, because it will lead future researchers astray.
Point 1: it isn't just "similar to Clifford algebra". It really IS Clifford algebra.
Point 2: by a chance quirk of algebra, it may well be that this particular Clifford algebra happens to be isomorphic to the complex quaternions, but this really is just a coincidence. Any such isomorphism will preserve the algebraic structure, but will lose the underlying geometry and motivation.
Point 3: this matters. Dirac's original theory can be extended very easily to
- curved space and Einstein's General Relativity
- asymmetric metrics, via Hannabuss's extension of Clifford algebras, and it may thus provide a model of other real physical features such as perhaps the weak interaction.
However, these extensions are ONLY apparent when the original GEOMETRIC origin of the algebra is kept obvious. If the algebra is treated as complex quaternions, or some other algebraic isomorph such as an exterior algebra, then they are lost.
Please see my essay, (1366), for more details.
Best wishes
Alan H.