A Clifford Algebra Lagrangian Formalism in Minkowski Spacetime

Using tools introduced in previous chapters, particularly the concept of Clifford and spin-Clifford bundles (and the representations of sections of the spin-Clifford bundles as equivalence classes of sections the Clifford bundle), extensor fields and the Dirac operator we give an unified and original approach to the Lagrangian field theory in Minkowski spacetime with special emphasis on the Maxwell and Dirac-Hestenes fields. We derive for these fields their canonical energy-momentum extensor fields and also their angular momentum and spin momentum extensor fields. In particular we show that the antisymmetric part of the canonical energy-momentum tensor is the “source” of spin of the field. Several nontrivial exercises are solved with details in order to help the reader to familiarize with the formalism and to make contact with standard formulations of field theory.