How `Complex' is the Dirac Equation?

Details How `Complex' is the Dirac Equation? How `Complex' is the Dirac Equation?

1998-10-14

arxiv.org/abs/hep-th/9810093v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Latex

Scientific paper

A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over a simple non-division algebra. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the transformation properties of the usual complex Dirac spinor. As an application, we show that there exists an algebra of automorphisms of the complex Dirac spinor that leave the transformation properties of its eight real components invariant under any given Lorentz transformation. Interestingly, the representation of the Lorentz group presented here has a natural embedding in SO(3,3) instead of the conformal symmetry SO(2,4).

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