  These notes explain recent developments concerning chiral anomalies and
hamiltonian quantization, their relation to the theory of gerbes, and
extensions of generalized loop algebras using the residue calculus of
pseudodifferential operators. The renormalization of the Dirac field, leading
to Schwinger terms in equal time commutation relations, is treated in a
mathematically rigorous manner. The same renormalization can be used to prove
the existence of S-operator in background field problems.
