  In this talk I want to explain the operator substractions needed to
renormalize gauge currents in a second quantized theory. The case of space-time
dimensions $3+1$ is considered in detail. In presence of chiral fermions the
renormalization effects a modification of the local commutation relations of
the currents by local Schwinger terms. In $1+1$ dimensions on 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. We extend our method to the spatial components of currents. Since
the bose-fermi interaction hamiltonian is of the form $j^k A_k$ (in the
temporal gauge) we get a new renormalization scheme for the interaction. The
idea is to define a field dependent conjugation for the fermi hamiltonian in
the one-particle space such that after the conjugation the hamiltonian can be
quantized just by normal ordering prescription.
