Concrete Fock representations of Mickelsson-Faddeev-like algebras

TL;DR

This paper constructs Fock modules for a classical version of the Mickelsson-Faddeev algebra, overcoming previous obstacles by omitting an inhomogeneous term, and explores their relation to higher-dimensional Virasoro algebra actions.

Contribution

It introduces explicit Fock modules for a classical MF algebra variant and analyzes their structure and symmetries, providing new representations.

Findings

Constructed explicit Fock modules for the classical MF algebra.

Demonstrated the intertwining action of higher-dimensional Virasoro algebra.

Showed that omitting the inhomogeneous term enables Fock representations.

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.