Concrete Fock representations of Mickelsson-Faddeev-like algebras

Abstract

The Mickelsson-Faddeev (MF) algebra can naturally be embedded in a non-Lie algebra, which suggests that it has no Fock representations. The difficulties are due to the inhomogeneous term in the connection's transformation law. Omitting this term yields a ``classical MF algebra'', which has other abelian extensions that do possess Fock modules. I explicitly construct such modules and the intertwining action of the higher-dimensional Virasoro algebra.