A Model of Unified Gauge Interactions

Abstract

Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all particle types. The algebra of the generators for infinitesimal transformations of these fields directly constructs the Minkowski metric \emph{within} the internal group space as a consequence of non-vanishing commutation relations between generators that carry space-time indexes. In addition, the generators have a fundamental matrix representation that includes Lorentz transformations within a group that unifies internal gauge symmetries generated by a set of hermitian generators for SU(3)$\times$SU(2)$\times$U(1), and nothing else. The construction of linearly independent internal SU(3) and SU(2) symmetry groups necessarily involves the mixing of three generations of the mass eigenstates labeling the (massive) representations of the linear spinor fields. The group algebra also provides a mechanism for the dynamic mixing of massless particles of differing "transverse mass" eigenvalues conjugate to the affine parameter labeling translations along their light-like trajectories. The inclusion of a transverse mass generator is necessary for group closure of the extended Poincare algebra, but its eigenvalue must vanish for massive particle representations. A unified set of space-time group transformation operations along with internal gauge group symmetry operations for linear spinor fields will be demonstrated in this paper.