Analysis in space-time bundles, II. The spinor and form bundles

Abstract

The structures of the spin and form bundles over the universal cosmos M̃, and their relations with corresponding bundles over the Minkowski space M 0 canonically imbedded in M̃, are treated. Wave equations covariant with respect to the causal group G of M̃ are studied, their solution manifolds and other stable (essentially positive-energy) invariant subspaces of the section spaces of the bundles are determined, and the indecomposability of relevant invariant subspace chains is shown. Explicit parallelizations of the bundles are applied to the Dirac and Maxwell equations on M̃. A basis for spinor fields that diagonalizes a complete set of K̃-covariant quantum numbers (K̃ = maximal essentially compact subgroup of G̃) is developed. Local multilinear invariants of bundles over M̃ are treated and specialized to convergent mathematical versions of the Fermi and Yukawa interaction Lagrangians that are G̃-invariant for the appropriate conformal weights.