Advertisement

Communications in Mathematical Physics

, Volume 143, Issue 3, pp 577–589 | Cite as

The realm of the vacuum

  • Detlev Buchholz
  • Rainer Wanzenberg
Article

Abstract

The spacelike asymptotic structure of physical states in local quantum theory is analysed. It is shown that this structure can be described in terms of a vacuum state if the theory satisfies a condition of timelike asymptotic abelianess. Theories which violate this condition can have an involved asymptotic vacuum structure as is illustrated by a simple example.

Keywords

Neural Network Physical State Complex System Nonlinear Dynamics Quantum Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848–861 (1964)CrossRefGoogle Scholar
  2. 2.
    Borchers, H.J., Haag, R., Schroer, B.: The vacuum state in quantum field theory. Nuovo Cimento29, 148–162 (1963)Google Scholar
  3. 3.
    Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1–54 (1982)CrossRefGoogle Scholar
  4. 4.
    Horuzhy, S.S.: Introduction to algebraic quantum field theory. Dordrecht, Boston, London: Kluwer 1990Google Scholar
  5. 5.
    Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics. II. Berlin, Heidelberg, New York: Springer 1981Google Scholar
  6. 6.
    Berberian, S.K.: Lectures in functional analysis and operator theory. Graduate Texts in Mathematics, Vol. 15. Berlin, Heidelberg, New York: Springer 1974Google Scholar
  7. 7.
    Buchholz, D.: Harmonic analysis of local operators. Commun. Math. Phys.129, 631–641 (1990)CrossRefGoogle Scholar
  8. 8.
    Borchers, H.J.: On the vacuum state in quantum field theory. II. Commun. Math. Phys.1, 57–79 (1965)CrossRefGoogle Scholar
  9. 9.
    Roepstorff, G.: Coherent photon states and spectral condition. Commun. Math. Phys.19, 301–314 (1970)CrossRefGoogle Scholar
  10. 10.
    Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers. Oxford at the Clarendon Press 1960Google Scholar
  11. 11.
    Borchers, H.J., Buchholz, D.: The energy momentum spectrum in local field theories with broken Lorentz symmetry. Commun. Math. Phys.97, 169–185 (1985)CrossRefGoogle Scholar
  12. 12.
    Wanzenberg, R.: Energie und Präparierbarkeit von Zuständen in der lokalen Quantenfeldtheorie. Diplomarbeit, Hamburg 1987Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Detlev Buchholz
    • 1
  • Rainer Wanzenberg
    • 2
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Federal Republic of Germany
  2. 2.Institut für Hochfrequenztechnik, Fachgebiet Theorie Elektromagnetischer FelderTechnische Hochschule DarmstadtDarmstadtFederal Republic of Germany

Personalised recommendations