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Symmetry Reduction Of Quasi-Free States, Charles G. Torre

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Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein–Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincaré group consisting of a …