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Communications in Mathematical Physics

, Volume 85, Issue 1, pp 49–71 | Cite as

The physical state space of quantum electrodynamics

  • Detlev Buchholz
Article

Abstract

Starting from the fact that electrically charged particles are massive, we derive a criterion which characterizes the state space of quantum electrodynamics. This criterion clarifies the special role of the electric charge amongst the uncountably many superselection rules in quantum electrodynamics and provides a basis for a general analysis of the infrared problem. Within this framework we establish the existence of asymptotic electromagnetic fields in all charge-sectors, find a general characterization of infra-particles and introduce a notion of asymptotic completeness.

Keywords

Quantum Electrodynamic Background Field Local Observable Asymptotic Completeness Superselection Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Jauch, J.M., Rohrlich, F.: The theory of photons and electrons. Berlin, Heidelberg, New York: Springer 1976CrossRefGoogle Scholar
  2. 2.
    Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics. I. Commun. Math. Phys.23, 199 (1971)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Strocchi, F., Wightman, A.S.: Proof of the charge superselection rule in local relativistic quantum field theory. J. Math. Phys.15, 2198 (1974)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Fröhlich, J., Morchio, G., Strocchi, F.: Infrared problem and spontaneous breaking of the Lorentz group in QED. Phys. Lett.89B, 61 (1979)ADSCrossRefGoogle Scholar
  5. 5.
    Symanzik, K.: Lectures on Lagrangian quantum field theory. DESYT-71Google Scholar
  6. 6.
    Haag, R., Kastler, D.: An algebraic approach to field theory. J. Math. Phys.5, 848 (1964)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Borchers, H.J., Buchholz, D.: To be published. For a sketch of the proof see [17]Google Scholar
  8. 8.
    Bisognano, J.J., Wichmann, E.: On the duality condition for a hermitean scalar field. J. Math. Phys.16, 985 (1975)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Haag, R.: Lille Conference 1957 «Les problèmes mathématiques de la théorie quantique des champs». Paris: Editions du CNRS 1959Google Scholar
  10. 10.
    Borchers, H.J.: Energy and momentum as observables in quantum field theory. Commun. Math. Phys.2, 49 (1966)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Sakai, S.:C*-algebras andW*-algebras. Berlin, Heidelberg, New York: Springer 1971CrossRefGoogle Scholar
  12. 12.
    Buchholz, D.: Collision theory for massless Bosons. Commun. Math. Phys.52, 147 (1977)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Borchers, H.J.: A remark on a theorem of B. Misra. Commun. Math. Phys.4, 315 (1967)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Borchers, H.J.: On the converse of the Reeh-Schlieder theorem. Commun. Math. Phys.10, 269 (1968)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Borchers, H.J.: On groups of automorphisms with semi-bounded spectrum. Paris: Editions du CNRS No. 181, 1970Google Scholar
  16. 16.
    Sadowski, P., Woronowicz, S.L.: Total sets in quantum field theory. Rep. Math. Phys.2, 113 (1971)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kraus, K., Polley, L., Reents, G.: Models for infrared dynamics. I. Classical currents. Ann. Inst. H. Poincaré26, 109 (1977)ADSMathSciNetGoogle Scholar
  19. 19.
    Schroer, B.: Infrateilchen in der Quantenfeldtheorie. Fortschr. Physik11, 1 (1963)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Araki, H., Haag, R.: Collision cross sections in terms of local observables. Commun. Math. Phys.4, 77 (1967)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Buchholz, D.: In: “Proceedings of the international conference on operator algebras, ideals and their applications in theoretical physics, Leipzig 1977”. Leipzig: Teubner 1978Google Scholar
  22. 22.
    Fröhlich, J.: On the infrared problem in a model of scalar electrons and massless scalar Bosons. Ann. Inst. H. Poincaré19, 1 (1973)MathSciNetzbMATHGoogle Scholar
  23. 22a.
    Fröhlich, J., Morchio, G., Strocchi, F.: Charged sectors and scattering states in quantum electrodynamics. Ann. Phys.119, 241 (1979)ADSMathSciNetCrossRefGoogle Scholar
  24. 23.
    Roepstorff, G.: Coherent photon states and spectral condition. Commun. Math. Phys.19, 301 (1970)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 24.
    Gervais, J.L., Zwanziger, D.: Derivation from first principles of the infrared structure of quantum electrodynamics. Phys. Lett.94B, 389 (1980)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Detlev Buchholz
    • 1
  1. 1.II. Institute of Theoretical PhysicsUniversity of HamburgHamburgGermany

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