63 research outputs found
Schwinger terms, gerbes, and operator residues
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.Comment: Lectures given at the Banach Center symposium "Differential Geometry
and Mathematical Physics", May 15 - 23, 1995. This is an AMS-TEX file. 18
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Boundary currents and hamiltonian quantization of fermions in background fields
The current algebra generated by fermions coupled to external gauge
potentials and metrics on a manifold with boundary is discussed. It is shown
that the previous methods, based on index theory arguments and used in the case
without boundaries, carry over to the present problem. The resulting current
algebra is the same as obtained from a quantization of bosonic Chern-Simons
theories on space-times with nonempty boundaries. This means that also in the
fermionic setting the construction is 'holographic', the Schwinger terms reside
on the boundary.Comment: 8 pages AmsTex, no figure
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