  It is well known how to define the operator $Q$ for the total charge (i.e.,
positron number minus electron number) on the standard Hilbert space of the
second-quantized Dirac equation. Here we ask about operators $Q_A$ representing
the charge content of a region $A\subseteq \mathbb{R}^3$ in 3d physical space.
There is a natural formula for $Q_A$ but, as we explain, there are difficulties
about turning it into a mathematically precise definition. First, $Q_A$ can be
written as a series but its convergence seems hopeless. Second, we show for
some choices of $A$ that if $Q_A$ could be defined then its domain could not
contain either the vacuum vector or any vector obtained from the vacuum by
applying a polynomial in creation and annihilation operators. Both observations
speak against the existence of $Q_A$ for generic $A$.
