Zeros and points of discontinuity of the commutator function of the free Dirac field

The properties of the commutator function of the free electron Dirac field, zeros of which respond to the independent measurements of the electron charge density in two different points of the space-time, are discussed. The established properties of one-space dimensional commutator function D(x; t) in the discrete representation, show the dependency of the number and location of its zeros and points of discontinuity on the value of normalizing factor. In this connection, the following new property of the commutator function is found: the length of the time interval containing at least one zero of D(x; t) depends on the relation between the value of the normalizing factor and the Compton wavelength of the electron.