  In this talk I want to explain the operator substractions needed to
regularize gauge currents in a second quantized theory. The case of space-time
dimension $3+1$ is considered in detail. In presence of chiral fermions the
regularization effects a modification of the local commutation relations of the
currents by local Schwinger terms. In $1+1$ dimensions one gets the usual
central extension (Schwinger term does not depend on background gauge field)
whereas in $3+1$ dimensions one gets an anomaly linear in the background
potential.
