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Teoreticheskaya i Matematicheskaya Fizika, 1984, Volume 59, Number 1, Pages 28–48
(Mi tmf4703)
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This article is cited in 23 scientific papers (total in 23 papers)
Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them
A. V. Voronin, V. N. Sushko, S. S. Horuzhy
Abstract:
In connection with the physical problem of describing vacuum
superselection rules in quantum field theory, a study is made of
some properties of Op* algebras, namely, the structure of their
commutants and invariant and reducing subspaces and vector states
on such algebras. For this, a formalism is developed that uses
intertwining operators of Hermitian representations of a *
algebra. The formalism is used to obtain a number of new
properties of the commutants of Op* algebras, and a description is
given of classes of subspaces the projection operators onto which
lie in the strong or weak commutant. A study is made of the
correspondence between vector states on the Op* algebra $\mathscr
P$ and on its associated yon Neumann algebra $R=({\mathscr
P_w}^{'})^{'}$; generalizations are found of the class of
self-adjoint Op* algebras for which a detailed investigation of
vector states can be made. Classes of weakly regular, strongly
regular, and completely regular vectors for which the properties
of states on $\mathscr P$ approach closer and closer to states on
$R$ are identified and studied.
Received: 09.09.1983
Citation:
A. V. Voronin, V. N. Sushko, S. S. Horuzhy, “Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them”, TMF, 59:1 (1984), 28–48; Theoret. and Math. Phys., 59:1 (1984), 335–350
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https://www.mathnet.ru/eng/tmf4703 https://www.mathnet.ru/eng/tmf/v59/i1/p28
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Abstract page: | 379 | Full-text PDF : | 107 | References: | 37 | First page: | 1 |
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