Localizing the relativistic electron

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator x. It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density (rho(x, t), j(x, t)/c) is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive energy states. A suitable spin operator can be diagonalized at the same time.