11,041 research outputs found
Symmetry Reduction of Quasi-Free States
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 quantum gravity model.Comment: 18 page
Classification of integrable discrete Klein-Gordon models
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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