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

Details Hilbert space cocycles as representations of $(3+1)-$ D current algebras Hilbert space cocycles as representations of $(3+1)-$ D current algebras

1992-10-13

arxiv.org/abs/hep-th/9210069v1

Lett.Math.Phys.28:97-106,1993

Physics

High Energy Physics

High Energy Physics - Theory

This is an AMSTEX file, 10 pages. It was written using

Scientific paper

10.1007/BF00750302

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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