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It is proposed that instead of normal representations one should look atcocycles of group extensions valued in certain groups of unitary operatorsacting in a Hilbert space (e.g the Fock space of chiral fermions), when dealingwith groups associated to current algebras in gauge theories in $3+1$space-time dimensions. The appropriate cocycle is evaluated in the case of thegroup of smooth maps from the physical three-space to a compact Lie group. Thecocyclic representation of a component $X$ of the current is obtained throughtwo regularizations, 1) a conjugation by a background potential dependentunitary 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 spaceusing the usual normal ordering subtraction.Comment: This is an AMSTEX file, 10 pages. It was written usin

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