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Hilbert space cocycles as representations of $(3+1)-$ D current algebras | | Jouko Mickelsson
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13 Oct 1992 | | Journal: | Lett. Math. Phys. 28 (1993) 97-106 | | Subject: | hep-th | | 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. | | Source: | arXiv, hep-th/9210069 | | Services: | Forum | Review | PDF | Favorites | |
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