On the Theory of the Electron and Positive

In this paper we develop Dirac's suggestions for the interpretation of his theory of the electron to give a consistent theory of electrons and positives. In Section 1, we discuss the physical interpretation of the theory, the limits which it imposes on the spatiotemporal description of a system and in particular on the localizability of the electron. In Section 2, we set up the corresponding formalism, introducing wave functions to describe the state of the electrons and positives in the system, and constructing operators to represent the energy, charge and current density, etc. It is shown that the theory is Lorentz invariant, and has just that invariance under contact transformations which the physical interpretation requires. The electromagnetic interaction of the electrons and positives is formulated, and certain ambiguities which arise here are discussed. In Section 3, it is shown that in all problems to which the Dirac equation is directly applicable it gives the correct energy levels for an electron, and the correct radiative and collision transition probabilities. In these problems the wave functions are constructed from the solutions of the Dirac equation. In Section 4, we discuss certain problems which have no analogue in the original Dirac theory of the electron, show that a certain part of the energy of an electromagnetic field in general resides in the electrons and positives, and consider the extent to which, in the present state of theory, this can be detected by experiment. For two charges within a Compton wave-length of each other the law of force is not quite Coulomb's law. The deviations though small should in principle be detectable when protons are scattered in hydrogen.