On the Limitations of the Theory of the Positron

Abstract

In a recent paper Dirac has suggested a further development of his theory of the positron. Dirac here considers the operators corresponding to charge and current density for a system of electrons in which nearly all the negative energy states are full, and shows that in the presence of an arbitrary external electromagnetic field these operators may be divided into two terms: one of these is infinite, and depends on the field but not on the state of the electrons; the other is finite and determinate, and depends on the field and on the electron state. Dirac makes the suggestion that these second terms be regarded as giving the charge and current density of the electron-positron distribution (epd): i.e., that the formalism of his theory of the electron be modified by the subtraction from the operators for charge and current density of the infinite and field-dependent terms. This modification leaves unaltered the Lorentz and gauge invariance of the theory and the validity of the conservation law for charge and current. Because, however, the way in which the operators are to be modified depends upon the value of the electromagnetic field, the method is not readily extended to take account of the field produced by the epd; on the other hand, it gives for the charge and current induced in the epd by an external field finite and definite results, and thus constitutes in this respect a true theoretical advance.