Unitary positive energy representations of the gauge group

Abstract

We investigate the positive energy representations (also called highest weight representations) of the gauge groupC∞ (Tv,G0),G0 being a compact simple Lie group, and discuss their unitarity, using the technique of Verma modules constructed from generalized loop algebras (a simple generalization of Kac-Moody affine Lie algebras). We show that the unitarity of the representation imposes severa restrictions in it. In particular, we show, as a part of a more general result, that the gauge group does not admit faithful unitary positive energy representations.