A new approach to the representation of the Lorentz group on the spinors
Imposition of a triple product form of the canonical anticommutation
relations on the natural basis defines a triple product making complex n-space
into a Cartan factor of type 4. This Jordan structure is used to construct
3- and 4-dimensional representations of the Lorentz group corresponding
respectively to the relativistic transformations of the electromagnetic field
and the Lorentz space-time transformations. The self-adjoint part of the
latter is a reducible spin 1/2 representation which gives rise to a spin 1
representation in the space of determinant preserving maps. This suggests
that the spin factor of dimension 4 can be used to represent the two types
of elementary particles in nature.
(This paper has appeared in Foundations of Physics
31 (2001), 1733-1766)
Yaakov Friedman <friedman@avoda.jct.ac.il>
Bernard Russo <brusso@math.uci.edu>