Relativistic Particles in External Fields

Axiomatic field theories suffer from a lack of nontrivial examples and especially of realistic ones. This paper explores an enlarged system of basic assumptions that encompasses the case of external fields. Then the Dirac theory of the hydrogen atom, for example, becomes both an example and a clue for further postulates. For nonrelativistic (Galilean) physics, a set of assumptions called presymmetry was found to account for the general features of empirically verified theories. In this paper those assumptions of presymmetry that seem reasonably extendable to the case of a Poincaré-covariant algebra of observation procedures are found to agree with properties of the theory of an electron-positron field in an external electromagnetic field. The full structure of the algebra $\mathcal{O}$ of observation procedures remains to be explored, with the hope of finding additional structure in theories of interacting fields. Another motivation of more immediate interest is the desire for a general set of constraints in describing systems, typified by the hydrogen atom, in which one part of the system is sufficiently heavy to be idealized as a source of an external field, while the other has relativistic velocities.