Hilbert space cocycles as representations of (3 + 1)-d current algebras

1992/10/13 by Jouko Mickelsson · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #hep-th

paper · pdf · doi:10.1007/bf00750302

published as Lett.Math.Phys.28:97-106,1993 · This is an AMSTEX file, 10 pages. It was written using

arxiv created 1992/10/13 · openalex publication_date 1993/06/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups associated to current algebras in gauge theories in 3+1 space-time dimensions. The appropriate cocycle is evaluated in the case of the group of smooth maps from the physical three-space to a compact Lie group. The cocyclic representation of a component X of the current is obtained through two regularizations, 1) a conjugation by a background potential dependent unitary operator h_A, 2) by a subtraction -h_A^-1\Cal L_X h_A, where \Cal L_X is a derivative along a gauge orbit. It is only the total operator h_A^-1 Xh_A-h_A^-1\Cal L_X h_A which is quantizable in the Fock space using the usual normal ordering subtraction.

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