$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.
Teoretičeskaâ i matematičeskaâ fizika, Tome 82 (1990) no. 3, pp. 323-330
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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.
@article{TMF_1990_82_3_a0,
author = {A. V. Voronin and S. S. Horuzhy},
title = {$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {323--330},
publisher = {mathdoc},
volume = {82},
number = {3},
year = {1990},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1990_82_3_a0/}
}
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/