Schwinger Terms and Cohomology of Pseudodifferential Operators

Details Schwinger Terms and Cohomology of Pseudodifferential Operators Schwinger Terms and Cohomology of Pseudodifferential Operators

1994-10-04

arxiv.org/abs/hep-th/9410016v1

Commun.Math.Phys.175:203-220,1996

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, plain tex

Scientific paper

10.1007/BF02101630

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.

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