Schwinger Terms and Cyclic Cohomology

Abstract

Recently, Schwinger terms seem to be playing an important role in quantum field theory and its application to mathematical problems. The present author pointed out (in MSRI and Iowa talks in 1985, see [1]) the mathematically canonical nature of Schwinger terms, namely they are an example of the cyclic 1-cocyle, which has been developed by Connes [8] in the framework of non-commutative geometry. This identification of Schwinger terms as a cyclic cocycle has been noted also by Carey and Hannabuss [7]. The purpose of the present article is to give an expository account of the identification of Schwinger terms as a cyclic co-cycle. It turns out that it has a close connection with the article of Kostant and Sternberg [10] in the present conference.