RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (2462 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tmf4159
• http://mi.mathnet.ru/eng/tmf/v4/i3/p341

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers

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
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
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
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
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
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
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
8. S. S. Horuzhy, “Superposition principle in Algebraic quantum theory”, Theoret. and Math. Phys., 23:2 (1975), 413–421
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
10. V. N. Sushko, “Fermionization of the $(\sin\varphi)_2$ interaction in a box”, Theoret. and Math. Phys., 37:2 (1978), 949–969
11. K. Yu. Dadashyan, S. S. Horuzhy, “Algebras of observables of the free Dirac field”, Theoret. and Math. Phys., 36:2 (1978), 665–675
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
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
•  Number of views: This page: 231 Full text: 101 References: 16 First page: 1