Schwinger Terms and Cohomology of Pseudodifferential Operators

Abstract

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component.

19 pages, plain tex

References in corpus (3)

• Fermion Current Algebras and Schwinger Terms in 3+1 Dimensions
• (3+1)-Dimensional Schwinger Terms and Non-commutative Geometry
• Higher-Dimensional Loop Algebras, Non-Abelian Extensions and p-Branes

Cited by in corpus (4)

• Anomalies and Schwinger terms in NCG field theory models
• Vacuum polarization and the geometric phase: Gauge invariance
• Classical Mechanics and geometric Quantization on an Infinite Dimensional Disc and Grassmannian
• On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations