Skip to main content
SpringerLink
Log in

Decoherence: A Dynamical Approach to Superselection Rules?

  • Conference paper
  • First Online:
Relativistic Quantum Measurement and Decoherence

Part of the book series: Lecture Notes in Physics ((LNP,volume 559))

Abstract

It is well known that the dynamical mechanism of decoherence may cause apparent superselection rules, like that of molecular chirality. These ‘environment-induced’ or ‘soft’ superselection rules may be contrasted with ‘hard’ superselection rules, like that of electric charge, whose existence is usually rigorously demonstrated by means of certain symmetry principles. We address the question of whether this distinction between ‘hard’ and ‘soft’ is well founded and argue that, despite first appearance, it might not be. For this we first review in detail some of the basic structural properties of the spaces of states and observables in order to establish a fairly precise notion of superselection rules. We then discuss two examples: 1.) the Bargmann superselection rule for overall mass in ordinary quantum mechanics, and 2.) the superselection rule for charge in quantum electrodynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aharonov Y., Susskind L. (1967): Charge Superselection Rule. Phys. Rev. 155, 1428–1431

    Article  ADS  Google Scholar 

  2. Araki H. (1980): A Remark on the Machida-Namiki Theory of Measurement. Prog. Theo. Phys. 64, 719–730

    MATH  ADS  MathSciNet  Google Scholar 

  3. Bargmann V. (1964): Note on Wigner’s Theorem on Symmetry Operations. Jour. Math. Phys. 5, 862–868

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Bogolubov N.N., Logunov A.A., Oksak A.I., Todorov I.T. (1990): General Principles of Quantum Field Theory, (Kluwer, Dordrecht).

    MATH  Google Scholar 

  5. Buchholz D. (1982): The Physical State Space of Quantum Electrodynamics. Commun. Math. Phys. 85, 49–71

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Dirac P.A.M. (1930): The Principles of Quantum Mechanics (Clarendon Press, Oxford)

    MATH  Google Scholar 

  7. Dixmier J. (1981): Von Neumann Algebras (North Holland, Amsterdam)

    MATH  Google Scholar 

  8. Dominguez A.E., Kozameh C.N., Ludvigsen M. (1997): Superselection Sectors in Asymptotic Quantization of Gravity, gr-qc/9609071

    Google Scholar 

  9. Galindo A., Pascual P. (1990): Quantum Mechanics I (Springer, Berlin)

    MATH  Google Scholar 

  10. Galindo A., Morales A., Nunez-Lagos R. (1962): Superselection Principle and Pure States of n-Identical Particles. Jour. Math. Phys. 3, 324–328

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. Gervais J.L., Zwanziger D. (1980): Derivation From First Principles of the InfraredStructure of Quantum Electrodynamics. Phys. Lett. B 94, 389–393

    Article  ADS  Google Scholar 

  12. Giulini D. (1995): Asymptotic Symmetry Groups of Long-Ranged Gauge Configurations. Mod. Phys. Lett A 10, 2059–2070

    Article  ADS  MathSciNet  Google Scholar 

  13. Giulini D. (1996): On Galilei Invariance andthe Bargmann Superselection Rule. Ann. Phys. (NY) 249, 222–235

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Giulini D. (1995): Quantum Mechanics on Spaces with Finite Fundamental Group. Helv. Phys. Acta 68, 438–469

    MATH  MathSciNet  Google Scholar 

  15. Giulini D., Kiefer C., Zeh H.D. (1995): Symmetries, Superselection Rules, and Decoherence. Phys. Lett. A 199, 291–298

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Giulini D, Joos E., Kiefer C., Kupsch J., Stamatescu I.-O., Zeh H.-D. (1996): Decoherence and the Appearance of a Classical World in Quantum Theory, (Springer, Berlin)

    MATH  Google Scholar 

  17. Haller K. (1978): Gupta-Bleuler condition and infrared-coherent states. Phys.Rev. D 18, 3045–3051

    Article  ADS  Google Scholar 

  18. Hartle J.B., Taylor J.R. (1969): Quantum Mechanics of Paraparticles. Phys. Rev. 178, 2043–2051

    Article  ADS  Google Scholar 

  19. Hepp K. (1972): Quantum Theory of Measurement and Macroscopic Observables. Helv. Phys. Acta 45, 237–248

    Google Scholar 

  20. Isham C.J. (1995): Lectures on Quantum Theory. (Imperial College Press)

    Google Scholar 

  21. Jackson J.D. (1975) Classical Electrodynamics, second edition, (John Wiley & Sons, New York)

    MATH  Google Scholar 

  22. Jauch J.M. (1960): Systems of Observables in Quantum Mechanics. Helv. Phys. Acta 33, 711–726

    MATH  MathSciNet  Google Scholar 

  23. Jauch J.M., Misra B. (1961): Supersymmetries and Essential Observables. Helv. Phys. Acta 34, 699–709

    MATH  MathSciNet  Google Scholar 

  24. Joos E. (2000): Elements of Environmental Decoherence. In:Decoherence: Theoretical, Experimental and Conceptual Problems, Lecture Notes in Physics Vol. 538 (Springer, Berlin), eds. P. Blanchard et al.

    Chapter  Google Scholar 

  25. Kijowski J., Rudolph G., Thielmann A. (1997): Algebra of Observables and Charge Superselection Sectors for QED on the Lattice. Commun. Math. Phys. 188, 535–564

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Kupsch J. (2000): Mathematical Aspects of Decoherence. In: Decoherence: Theoretical, Experimental and Conceptual Problems, Lecture Notes in Physics Vol. 538 (Springer, Berlin), eds. P. Blanchard et al.

    Chapter  Google Scholar 

  27. Landsman N.P. (1995): Observation and Superselection in Quantum Mechanics. Stud. Hist. Phil. Mod. Phys. 26, 45–73

    Article  MathSciNet  Google Scholar 

  28. Messiah A.M., Greenberg O.W. (1964): Symmetrization Postulate and Its Experimental Foundation. Phys. Rev. 236, B 248–B 267

    MathSciNet  Google Scholar 

  29. Mirman R. (1969): Coherent Superposition of Charge States. Phys. Rev. 186, 1380–1383

    Article  ADS  Google Scholar 

  30. Pfeifer P. (1980): A simple model for irreversible dynamics from unitary time evolution. Helv. Phys. Acta 53, 410–415

    MathSciNet  Google Scholar 

  31. Primas H. (2000): Asymptotically disjoint quantum states. In: Decoherence: Theoretical, Experimental, and Conceptual Problems, Lecture Notes in Physics Vol. 538 (Springer, Berlin), eds. P. Blanchard et al.

    Chapter  Google Scholar 

  32. Raghunathan M.S. (1994): Universal Central Extensions. Rev. Math. Phys. 6, 207–225

    Article  MATH  MathSciNet  Google Scholar 

  33. Strocchi F., Wightman A.S. (1974): Proof of the Charge Superselection Rule in Local Relativistic Quantum Field Theory. Jour. Math. Phys. 15, 2198–2224; Erratum Ibid 17 (1976), 1930-1931

    Article  MathSciNet  ADS  Google Scholar 

  34. von Neumann J. (1931): Über Funktionen von Funktionaloperatoren. Ann. Math. (Princeton) 32 191–226

    Article  Google Scholar 

  35. Wick G.C., Wightman A.S., Wigner E.P. (1952): The Intrinsic Parity of Elementary Particles. Phys. Rev. 88, 101–105

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. Wick G.C., Wightman A.S., Wigner E.P. (1970): Superselection Rule for Charge. Phys. Rev. D 1 3267–3269

    Article  ADS  Google Scholar 

  37. Wightman, A.S. (1959): Relativistic Invariance and Quantum Mechanics (Notes by A. Barut). Nouvo Cimento, Suppl. 14, 81–94

    MathSciNet  Google Scholar 

  38. Wightman A.S., Glance N. (1989): Superselection Rules in Molecules. Nucl. Phys. B (Proc. Suppl.) 6, 202–206

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. Wightman A.S. (1995): Superselection Rules; Old andNew. Il Nuovo Cimento 110 B, 751–769

    MathSciNet  ADS  Google Scholar 

  40. Zuerk W. (1982): Environment-Induced Superselection Rules. Phys. Rev. D 26, 1862–1880

    Article  ADS  MathSciNet  Google Scholar 

  41. Zwanziger D. (1976): Physical States in Quantum Electrodynamics. Phys. Rev. D 14, 2570–2589

    Article  ADS  Google Scholar 

  42. Zwanziger D. (1978): Gupta-Bleuler and Infrared-Coherence Subsidiary Conditions. Phys. Rev. D 18, 3051–3057

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretische Physik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Domenico Giulini

Authors
  1. Domenico Giulini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Physics, University of Freiburg, Hermann-Herder-Strasse 3, 79104, Freiburg, Germany

    Heinz-Peter Breuer  & Francesco Petruccione  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Giulini, D. (2000). Decoherence: A Dynamical Approach to Superselection Rules?. In: Breuer, HP., Petruccione, F. (eds) Relativistic Quantum Measurement and Decoherence. Lecture Notes in Physics, vol 559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45369-5_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-45369-5_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41061-4

  • Online ISBN: 978-3-540-45369-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation