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Superselection rules; old and new

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Il Nuovo Cimento B (1971-1996)

Summary

This paper is a historical review of the development of the notion of superselection rule starting from the recognition in 1952 of the charge and univalence superselection rules. Some applications to environmentally induced superselection rules in the last decade are briefly described.

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References

  1. von Neumann J.,Mathematische Grundlagen der quantenmechanik (Julius Springer, Berlin) 1932;Mathematical Foundations of Quantum Mechanics, translated byR. T. Beyer (Princeton University Press, Princeton, N.J.) 1955, especially p. 167 of the original. I have translated «... es ist zweckmÄssig anzunehmen,...» as «... it is appropriate to assume,...» instead of Beyer’s «... it is convenient to assume, ...». My dictionary prefers «suitable for the object in view».

    MATH  Google Scholar 

  2. Yang C. N. andTiomno J.,Phys. Rev.,79 (1950) 495.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Zharkov G. F.,Sov. Phys. JETP,20 (1950) 492.

    Google Scholar 

  4. Orear J., Rosenfeld A. H. andSchluter R. A. (Editors),Proceedings of the International Conference, Nuclear Physics and the Physics of Fundamental Particles,September 17–22, 1951, sect. IIC. On the inversion properties of spin-(l/2) fields, see pp. 109–110, reported by Morris Scharff.

  5. Wick G. C., Wightman A. S. andWigner E. P.,Phys. Rev.,88 (1952) 101.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Cartan E.,LeÇons sur la théorie des spineurs I, II. Actualités scientifiques et industrielles (Hermann, Paris) 1938, pp. 643 and 701.

    Google Scholar 

  7. Hegerfeldt G. C., Kraus K. andWigner E. P.,J. Math. Phys.,9 (1968) 2029.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Aharanov Y. andSusskind L.,Phys. Rev.,155 (1967) 1428;158 (1967) 1237;Mermin R.,Phys. Rev.,186 (1969) 1380;Phys. Rev. D,1 (1970) 3349.

    Article  ADS  Google Scholar 

  9. Badurek G., Rauch H. andSummhammer J.,Physim B,151 (1988) 82.

    Article  ADS  Google Scholar 

  10. Wick G. C., Wightman A. S. andWigner E. P.,Phys. Rev. D,1 (1970) 3267.

    Article  ADS  Google Scholar 

  11. Newman M. H. A.,J. London Math. Soc.,17 (1942) 173.

    Article  MathSciNet  Google Scholar 

  12. Naber G. L.,The Geometry of Minkowski Space (Springer-Verlag, New York, NX) 1992, especially appendix B, pp. 226–239.

    Book  Google Scholar 

  13. Misner C. W., Thorne K. S. andWheeler J. A.,Gravitation (W. H. Freeman, San Francisco, Cal.) 1973, Chapt. 41,Spinors, pp. 1135–1165 especially sect. 41.5, pp. 1148–1150.

    Google Scholar 

  14. Bargmann V.,Ann. Math.,59 (1954) 1.

    Article  MathSciNet  MATH  Google Scholar 

  15. Wightman A. S.,Nuovo Cimento Suppl.,14 (1959) 81, especially p. 93. See alsoRelations de dispersion et particules élémentaires (Hermann, Paris) 1960, especially pp. 176–181.

    MathSciNet  Google Scholar 

  16. Wigner E. P. Group Theoretical Concepts in Elementary Particle Physics, edited byF. Gürsey (Academic Press, New York, N.Y.) 1965, pp. 37–80.

    Google Scholar 

  17. Jost R.,Helv. Phys. Acta,30 (1957) 409.

    MathSciNet  MATH  Google Scholar 

  18. Lee T. D. andWick G. C.,Phys. Rev.,148 (1966) 1385.

    Article  MathSciNet  ADS  Google Scholar 

  19. Jauch J. M.,Helv. Phys. Acta,34 (1961) 711.

    MathSciNet  Google Scholar 

  20. Wigner E. P. andYanase M. M.,Proc. Natl Acad. Sci. (USA),49 (1963) 910;Canad. J. Math.,16 (1964) 397.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Wehel A.,Rev. Mod. Phys.,50 (1978) 221, especially p. 248, strong subadditivity and Lieb’s theorem and p. 252, skew entropy and the Wigner-Yanase-Dyson conjecture.

    Article  ADS  Google Scholar 

  22. Wigner E. P.,Z. Phys.,133 (1952) 101.

    Article  MathSciNet  ADS  Google Scholar 

  23. Araki H. andYanase M.,Phys. Rev.,120 (1960) 622.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Haag R.,Ann. Phys. (Leipzig),11 (1963) 29.

    Article  MathSciNet  ADS  Google Scholar 

  25. Strocchi F. andWightman A. S.,J. Math. Phys.,15 (1974) 2198;17 (1976) 1930.

    Article  MathSciNet  ADS  Google Scholar 

  26. Haag R. andKastler D.,J. Math. Phys.,5 (1964) 548. The capsule treatment of the work of Haag, Kastler, Doplicher and Roberts in this section is given an extended exposition along with many further developments in the books [31] and [32].

    Article  MathSciNet  Google Scholar 

  27. Doplicher S., Haag R. andRoberts J.,Commun. Math. Phys.,23 (1971) 199;35 (1974) 49.

    Article  MathSciNet  ADS  Google Scholar 

  28. Doplicher S. andRoberts J.,Commun. Math. Phys.,131 (1990) 51.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Buchholz D. andFredenhagen K.,Commun. Math. Phys.,84 (1982) 1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Buchholz D.,Commun. Math. Phys.,85 (1982) 49.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. Haag R.,Local Quantum Physics Fields, Particles Algebras (Springer-Verlag, Berlin) 1992.

    Book  MATH  Google Scholar 

  32. Kastler D. (Editor),The Algebraic Theory of Superselection Sectors. Introduction and Recent Results (World Scientific, Singapore) 1990.

    Google Scholar 

  33. Omnès R.,The Interpretation of Quantum Mechanics (Princeton University Press, Princeton, N.J.) 1994.

    Google Scholar 

  34. Joos E. andZeh H.,Z. Phys. B,59 (1985) 223.

    Article  ADS  Google Scholar 

  35. Zurek W.,Phys. Rev. D,26 (1983) 1862.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Wightman A. S.,Some comments on the quantum theory of measurement, inProceedings of the International Workshop Probability Methods in Mathematical Physics, Certosa di Pontignano,Siena, Italy,6-11 May 1991, edited byF. Guerra,M. Loffredo andC. Marchioro (World Scientific, Singapore) 1992, pp. 411–438.

    Google Scholar 

  37. It is worth noting that the word chirality was first intorduced byLord Kelvin in the 1904 version of hisBaltimore Lectures on Molecular Dynamics and the Wave Theory of Light (Cambridge University Press, Warehouse, London) 1904, Appendix H, p. 619, where he says: «I call any geometrical figure, or group of points,chiral, and say that it has chirality if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself... » He also notes that such a pair of figures have been calledenantimorphs.

    MATH  Google Scholar 

  38. Amann A., inLarge-Scale Molecular Systems: Quantum and Stochastic Aspects. Beyond the Simple Molecular Picture, edited byW. Gaus, A. Blumen andA. Amann (Plenum, New York, N.Y.) 1991, pp. 3–32.

    Chapter  Google Scholar 

  39. Jona-Lasinio G., Martinelli F. andScoppola E.,Commun. Math. Phys.,80 (1981) 223.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. J. Funct. Anal.,63 (1985) 123.

  41. Claverie P. andJona-Lasinio G.,Phys. Rev. A,33 (1986) 2245.

    Article  ADS  Google Scholar 

  42. Anderson P. W.,Phys. Rev.,75 (1949) 1450L;76 (1949) 471A;76 (1949) 647.

    Article  ADS  Google Scholar 

  43. Indications of such a red-shift are also found in the static calculations ofMargenan H.,Phys. Rev.,76 (1949) 1423.

    Article  ADS  Google Scholar 

  44. Birnbaum G. andMaryott A. A.,Phys. Rev.,92 (1953) 270.

    Article  ADS  Google Scholar 

  45. Amann A., inFractals Quasi-Crystals, Chaos, Knots, and Algebraic Quantum Mechanics (Kluwer) 1988, pp. 305–325. See alsoWightman A. S. andGlance N.,Nucl. Phys. B (Proc. Suppl.),6 (1989) 202.

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  1. Department of Physics, Joseph Henry Laboratories, Princeton University, Jadwin Hall POB 708, 08544, Princeton, NJ, USA

    A. S. Wightman

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Wightman, A.S. Superselection rules; old and new. Nuov Cim B 110, 751–769 (1995). https://doi.org/10.1007/BF02741478

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  • DOI: https://doi.org/10.1007/BF02741478

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