Universal Schwinger cocycles of current algebras in (D+1)-dimensions: Geometry and physics

Abstract

We discuss the universal version of the Schwinger terms of current algebra (we call it the universal Schwinger cocycle) forp=3 (herep denotes the class of the Schatten idealI p , which is related to the (D+1) space-time dimensions byp=(D+1)/2) in detail, and give a conjecture of the general form of the cocycle for anyp. We also discuss the infinite charge renormalizations, the highest weight vector and state vectors forp=3. Last, we give brief comments on the problems caused by the difficulties to construct the measure of infinite-dimensional Grassmann manifolds.