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The commutator anomalies (Schwinger terms) of current algebras in $3+1$dimensions are computed in terms of the Wodzicki residue of pseudodifferentialoperators; the result can be written as a (twisted) Radul 2-cocycle for the Liealgebra of PSDO's. The construction of the (second quantized) current algebrais closely related to a geometric renormalization of the interactionHamiltonian $H_I=j_{\mu} A^{\mu}$ in gauge theory.Comment: 15 pages, updated version of a talk at the Baltic School in Field  Theory, September 199

Wodzicki residue and anomalies of current algebras