Wodzicki residue and anomalies of current algebras

Abstract

The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra of PSDO's. The construction of the (second quantized) current algebra is closely related to a geometric renormalization of the interaction Hamiltonian $H_I=j_{\mu }{A}^{\mu }$ in gauge theory.

15 pages, updated version of a talk at the Baltic School in Field Theory, September 1993

References in corpus (1)

• Hilbert space cocycles as representations of $(3+1)-$ D current algebras

Cited by in corpus (2)

• On the geometry of $Diff(S^1)-$pseudodifferential operators based on renormalized traces
• 3D Current Algebra and Twisted K Theory