Geodesic
$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 323-330 Cet article a éte moissonné depuis la source Math-Net.Ru

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According to the results of Part I [1], the only nontrivial difference between the vacuum struclures of $\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems is the effect of the infinite vacuum degeneracy in irreducible $\mathrm{Op}^*$ systems. For brevity, this effect is referred to as the “Borchers anomaly”, and is analyzed in detail by means of new mathematical tools – the recently introduced unbounded commutants of $\mathrm{Op}^*$ operators. A simple representation is obtained for the vacuum subspace of any field theory with cyclic vacuum in terms of the unbounded commutant of the field algebra, and from this representation a new necessary and sufficient condition for uniqueness of the vacuum is obtained. Some conditions for absence of the Borchers anomaly are derived, and a comparison which shows how these conditions improve the ones previously known is made. 
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     title = {$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_3_a0/}
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A. V. Voronin; S. S. Horuzhy. $\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.. Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/TMF_1990_82_3_a0/

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