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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_1984_59_1_a1,
     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},
     year = {1984},
     volume = {59},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a1/}
}
TY  - JOUR
AU  - A. V. Voronin
AU  - V. N. Sushko
AU  - S. S. Horuzhy
TI  - Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 28
EP  - 48
VL  - 59
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a1/
LA  - ru
ID  - TMF_1984_59_1_a1
ER  - 
%0 Journal Article
%A A. V. Voronin
%A V. N. Sushko
%A S. S. Horuzhy
%T Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 28-48
%V 59
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1984_59_1_a1/
%G ru
%F TMF_1984_59_1_a1
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/

[1] Frohlich J., Commun. Math. Phys., 47 (1976), 269–310 | DOI | MR

[2] Frohlich J., Lect. Notes Phys., 73, Berlin, 1978 | MR | Zbl

[3] Lassner G., Rep. Math. Phys., 3 (1972), 279–291 | DOI | MR

[4] Powers R. T., Commun. Math. Phys., 21 (1971), 85–124 | DOI | MR | Zbl

[5] Gudder S., Scruggs W., Pacific J. Math., 70 (1977), 369–382 | DOI | MR | Zbl

[6] Vasilev A. N., TMF, 2:2 (1970), 153–168 | MR

[7] Borchers H. J., Yngvason J., Commun. Math. Phys., 42 (1975), 231–252 | DOI | MR | Zbl

[8] Sushko V. N., Khoruzhii S. S., TMF, 4:2 (1970), 171–195 | MR

[9] Sushko V. N., Khoruzhii S. S., TMF, 8:3 (1971), 324–327 | MR | Zbl