11,041 research outputs found

    Symmetry Reduction of Quasi-Free States

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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 non-compact the group averaging prescription relies upon 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 non-compact subgroup of the Poincar\'e group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy T3{\bf T}^3 quantum gravity model.Comment: 18 page

    Classification of integrable discrete Klein-Gordon models

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    The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models. A new integrable example is found, its higher symmetry is presented.Comment: 12 pages, submitted to Physica Script
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