Geodesic
Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them
Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 28-48

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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. 
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     author = {A. V. Voronin and V. N. Sushko and S. S. Horuzhy},
     title = {Algebras of unbounded operators and vacuum superselection rules in quantum field theory. {I.} {Some} properties of {Op*-algebras} and vector states on them},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {28--48},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a1/}
}
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 59 (1984) no. 1, pp. 28-48. http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a1/