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TMF, 1970, Volume 4, Number 3, Pages 341–359 (Mi tmf4159)  

This article is cited in 13 scientific papers (total in 13 papers)

Vector states on algebras of observables and superselection rules II. Algebraic theory of superselection rules

V. N. Sushko, S. S. Horuzhy


Abstract: The methods and results of Part I are used to give a new and complete mathematical formuiation of superselectionrules. This is done first for very simple “diehotomic” superselection rules and then for arbitrary rules. Three fundamental physical conditions are formulated that are equivalent to one another and, taken together, give the abstract definition of a superselection rule. A number of new features of superselection rules is revealed. The most important are the following: 1) the superselection operators in the general case belong to the center of the global algebra of observables $R$; 2) the phenomenon of superselection rules exists and possesses the complete set of necessary physical properties only for the class of theories with a sufficient set of pure vector states (this concept was introduced and studied in Part I). It is established which forms of “continuous” superselection rules are possible and which are impossible in a physical theory. A coheren superselection sector is defined as a factorial type I representation of $R$. A generalization of the principle of superposigon is formulated and it is proved that it is satisfied in a coherent sector.

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English version:
Theoretical and Mathematical Physics, 1970, 4:3, 877–889

Bibliographic databases:

Received: 09.04.1970

Citation: V. N. Sushko, S. S. Horuzhy, “Vector states on algebras of observables and superselection rules II. Algebraic theory of superselection rules”, TMF, 4:3 (1970), 341–359; Theoret. and Math. Phys., 4:3 (1970), 877–889

Citation in format AMSBIB
\Bibitem{SusHor70}
\by V.~N.~Sushko, S.~S.~Horuzhy
\paper Vector states on algebras of observables and superselection rules
II.~Algebraic theory of superselection rules
\jour TMF
\yr 1970
\vol 4
\issue 3
\pages 341--359
\mathnet{http://mi.mathnet.ru/tmf4159}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464977}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 4
\issue 3
\pages 877--889
\crossref{https://doi.org/10.1007/BF01038302}


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    This publication is cited in the following articles:
    1. V. N. Sushko, S. S. Horuzhy, “Properties of $H$ images of vector states on algebras of observables”, Theoret. and Math. Phys., 8:3 (1971), 862–864  mathnet  crossref  mathscinet  zmath
    2. A. V. Bulinski, “On the classes of $C^*$ algebras that satisfy the Haag–Kastler axioms”, Theoret. and Math. Phys., 8:3 (1971), 865–869  mathnet  crossref  mathscinet  zmath
    3. V. N. Sushko, S. S. Horuzhy, “Local and asymptotic structure of quantum systems with superselection rules”, Theoret. and Math. Phys., 13:3 (1972), 1147–1160  mathnet  crossref  mathscinet
    4. V. N. Sushko, S. S. Horuzhy, “$H$-images of vector states and causal properties of local algebras”, Theoret. and Math. Phys., 15:2 (1973), 460–466  mathnet  crossref  zmath
    5. M. K. Polivanov, V. N. Sushko, S. S. Horuzhy, “Axioms of algebra of observables and the field concept”, Theoret. and Math. Phys., 16:1 (1973), 629–641  mathnet  crossref  zmath
    6. S. G. Kharatyan, “Von neumann algebras of observables with non-Abelian commutator algebra and superselection rules”, Theoret. and Math. Phys., 14:3 (1973), 227–232  mathnet  crossref  mathscinet  zmath
    7. Yu. M. Zinoviev, V. N. Sushko, “Physical symmetries in a theory of local observables of the $P$-class”, Theoret. and Math. Phys., 18:1 (1974), 9–18  mathnet  crossref  mathscinet  zmath
    8. S. S. Horuzhy, “Superposition principle in Algebraic quantum theory”, Theoret. and Math. Phys., 23:2 (1975), 413–421  mathnet  crossref  mathscinet  zmath
    9. K. Yu. Dadashyan, S. S. Horuzhy, “Simplicity of the quasilocal algebra of the system of canonical anticommutation relations with compact gauge group”, Theoret. and Math. Phys., 37:1 (1978), 837–842  mathnet  crossref  mathscinet
    10. V. N. Sushko, “Fermionization of the $(\sin\varphi)_2$ interaction in a box”, Theoret. and Math. Phys., 37:2 (1978), 949–969  mathnet  crossref  mathscinet
    11. K. Yu. Dadashyan, S. S. Horuzhy, “Algebras of observables of the free Dirac field”, Theoret. and Math. Phys., 36:2 (1978), 665–675  mathnet  crossref  mathscinet
    12. A. V. Voronin, V. N. Sushko, S. S. Horuzhy, “Algebras of unbounded operators and vacuum superselection rules in quantum field theory II. Mathematical structure of vacuum superselection rules”, Theoret. and Math. Phys., 60:3 (1984), 849–862  mathnet  crossref  mathscinet  zmath  isi
    13. A. V. Voronin, “Discrete vacuum superselection rule in Wightman theory with essentially self-adjoint field operators”, Theoret. and Math. Phys., 66:1 (1986), 8–19  mathnet  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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