Propagation in a complex Hilbert space, in a standard Quantum Mechanics or Quantum field Theory formulation, requires the propagator function to be a complex number. This prohibits what would otherwise be an obvious generalization to hypercomplex algebras. In order to achieve this generalization, we have to introduce a new layer to the theory, one with universal emanation involving hypercomplex algebras (trigintaduonions) that is hypothesized to project to the familiar complex Hilbert space propagation with associated fixed ...
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Propagation in a complex Hilbert space, in a standard Quantum Mechanics or Quantum field Theory formulation, requires the propagator function to be a complex number. This prohibits what would otherwise be an obvious generalization to hypercomplex algebras. In order to achieve this generalization, we have to introduce a new layer to the theory, one with universal emanation involving hypercomplex algebras (trigintaduonions) that is hypothesized to project to the familiar complex Hilbert space propagation with associated fixed elements (e.g., the emanator formalism projects out the observed constants and group structure of the standard model). The 'projection' is an induced mathematical construct, like having SU(3) on products of octonions, but here it will be the standard model U(1)xSU(2)xSU(3) on products of emanator trigintaduonions. Thus, in Book 7, last of the Physics Series, a unified variational formulation is posed, one that arrives at alpha as a natural structural element, and the standard model, among other things, uniquely specified by the condition of maximal information emanation.
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