The Cartan formalism in field theory

We consider a generalisation to field theory of the symplectic geometric approach to particle mechanics. This involves the definition of spacetime models; space and time as separate entities being taken as the primitive elements of the theory. Dynamical covariance and the CPT transformation of the Maxwell-Dirac and Maxwell-Schrödinger fields can then be discussed within the same formalism. A novel matrix formulation of the Schrödinger equation emerges which is a direct limit from the Dirac field