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TMF, 1990, Volume 82, Number 3, Pages 323–330 (Mi tmf5710)  

$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems. II. Structural differences: Borchers anomaly

A. V. Voronin, S. S. Horuzhy


Abstract: 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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English version:
Theoretical and Mathematical Physics, 1990, 82:3, 225–230

Bibliographic databases:

Document Type: Article
Received: 29.12.1988

Citation: A. V. Voronin, S. S. Horuzhy, “$\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems. II. Structural differences: Borchers anomaly”, TMF, 82:3 (1990), 323–330; Theoret. and Math. Phys., 82:3 (1990), 225–230

Citation in format AMSBIB
\Bibitem{VorHor90}
\by A.~V.~Voronin, S.~S.~Horuzhy
\paper $\mathrm{Op}^*$ and $\mathrm{C}^*$ dynamical systems.
II.~Structural differences: Borchers anomaly
\jour TMF
\yr 1990
\vol 82
\issue 3
\pages 323--330
\mathnet{http://mi.mathnet.ru/tmf5710}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1050284}
\zmath{https://zbmath.org/?q=an:0723.47039}
\transl
\jour Theoret. and Math. Phys.
\yr 1990
\vol 82
\issue 3
\pages 225--230
\crossref{https://doi.org/10.1007/BF01029215}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990EB42600001}


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