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 TMF, 1974, Volume 20, Number 2, Pages 177–180 (Mi tmf3812)

Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach

S. G. Kharatyan

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1974, 20:2, 751–753

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Citation: S. G. Kharatyan, “Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach”, TMF, 20:2 (1974), 177–180; Theoret. and Math. Phys., 20:2 (1974), 751–753

Citation in format AMSBIB
\Bibitem{Kha74} \by S.~G.~Kharatyan \paper Generalization of Wigner's theorem on symmetries in the $C^*$-algebraic approach \jour TMF \yr 1974 \vol 20 \issue 2 \pages 177--180 \mathnet{http://mi.mathnet.ru/tmf3812} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=464974} \zmath{https://zbmath.org/?q=an:0299.46055} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 20 \issue 2 \pages 751--753 \crossref{https://doi.org/10.1007/BF01037326}