We consider a model of a quantized fermion field that is based on the Dirac
equation in one dimensional space and re-examine how the fermion number of the
vacuum, or the vacuum charge, varies when an external potential is switched on.
With this model, fractionization of the vacuum charge has been illustrated in
the literature by showing that the external potential can change the vacuum
charge from zero to a fractional number. Charge conservation then appears
violated in this process. This is because the charge that has been examined in
this context is only a part of the total charge of the vacuum. The total charge
is conserved. It is not fractionalized unless the Dirac equation has a zero
mode. Two other confusing aspects are discussed. One is concerned with the
usage of the continuum limit and the other with the regularization of the
current operator. Implications of these aspects of the vacuum problem are
explored.
