  If a mathematical theory contains incompatible postulates then it is likely
that the theory will produce theorems or results that are contradictory. It
will be shown that this is the case with Dirac field theory. An example of such
a contradiction is the problem asociated with evaluating the Schwinger term. It
is generally known that different ways of evaluating this quantity yield
different results. It will be shown that the reason for this is that Dirac
field theory is mathematically inconsistent, i.e., it contains incompatible
assumptions or postulates. The generally accepted definition of the vacuum
state must be modified in order to create a consistent theory.
