Geodesic
Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 177-180 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On the basis of the abstract algebraic definition of a probability of transition between pure states the following generalization of Wigner's theorem is proved: the $C^*$-algebras of observables $\mathfrak A_1$ and $\mathfrak A_2$ are related by a symmetry transformation if and only if there exists a one-to-one mapping of the set of pure states over $\mathfrak A_1$ onto the set of pure states over $\mathfrak A_2$ that preserves the probability of the transition. 
@article{TMF_1974_20_2_a3,
     author = {S. G. Kharatyan},
     title = {Generalization of {Wigner's} theorem on symmetries in the $C^*$-algebraic approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {177--180},
     year = {1974},
     volume = {20},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a3/}
}
TY  - JOUR
AU  - S. G. Kharatyan
TI  - Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1974
SP  - 177
EP  - 180
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a3/
LA  - ru
ID  - TMF_1974_20_2_a3
ER  - 
%0 Journal Article
%A S. G. Kharatyan
%T Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1974
%P 177-180
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a3/
%G ru
%F TMF_1974_20_2_a3
S. G. Kharatyan. Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 20 (1974) no. 2, pp. 177-180. http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a3/

[1] E. Vigner, Teoriya grupp i ee prilozheniya k kvantovomekhanicheskoi teorii atomnykh spektrov, IL, 1961 | MR

[2] E. Roberts, P. Roepstoff, Commun. Math. Phys., 11 (1969), 94 | DOI

[3] R. Kadison, Topology, Suppl. 2, 3 (1965), 177 | DOI | MR | Zbl

[4] R. Kadison, Ann. Math., 54 (1951), 325 | DOI | MR | Zbl

[5] M. A. Naimark, Normirovannye koltsa, «Nauka», 1968 | MR | Zbl

[6] U. Ulhorn, Arkiv för Fysik, 27 (1963), 143