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

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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},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_20_2_a3/}
}
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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/