  In quantum theory, for a system with macroscopic wavefunction, the charge
density and current density are represented by non-commuting operators. It
follows that the anomaly $I=\partial_t \rho + \nabla \cdot \mathbf{j}$, being
essentially a linear combination of these two operators in the
frequency-momentum domain, does not admit eigenstates and has a minimum
uncertainty fixed by the Heisenberg relation $\Delta N \Delta \phi \simeq 1$
which involves the occupation number and the phase of the wavefunction. We give
an estimate of the minimum uncertainty in the case of a tunnel Josephson
junction made of Nb. Due to this violation of the local conservation of charge,
for the evaluation of the e.m. field generated by the system it is necessary to
use the extended Aharonov-Bohm electrodynamics. After recalling its field
equations, we compute in general form the energy-momentum tensor and the
radiation power flux generated by a localized oscillating source. The physical
requirements that the total flux be positive, negative or zero yield some
conditions on the dipole moment of the anomaly $I$.
