Communications in Mathematical Physics

, Volume 129, Issue 3, pp 631–641 | Cite as

Harmonic analysis of local operators

  • Detlev Buchholz


The spatial Fourier transforms of local operators are analysed. It is shown that the Fourier components for non-zero momentum form weakly square integrable functions in all states of finite energy. Moreover, there hold uniform bounds for the respectiveL2-norms. The relevance of this result is illustrated in collision theory.


Neural Network Fourier Fourier Transform Statistical Physic Complex System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Haag, R., Schroer, B.: Postulates of quantum field theory. J. Math. Phys.3, 248–256 (1962)CrossRefGoogle Scholar
  2. 2.
    Arveson, B.: The harmonic analysis of automorphism groups. In: Operator algebras and applications. I. Proceedings of Symposia in Pure Mathematics, Vol. 38. Providence: Am. Math. Soc. 1982Google Scholar
  3. 3.
    Buchholz, D., Wanzenberg, R.: In preparationGoogle Scholar
  4. 4.
    Araki, H.: Einführung in die axiomatische Quantenfeldtheorie. II. Lecture notes. ETH Zürich 1962.Google Scholar
  5. 5.
    Araki, H., Haag, R.: Collision cross sections in terms of local observables. Commun. Math. Phys.4, 77–91 (1967)CrossRefGoogle Scholar
  6. 6.
    Reed, M., Simon, B.: Methods of modern mathematical physics. II. Fourier analysis, self adjoitness. New York, San Francisco, London: Academic Press 1975Google Scholar
  7. 7.
    Lehmann, H., Symanzik, K., Zimmermann, W.: Zur Formulierung quantisierter Feldtheorien. Nuovo Cimento1, 205–225 (1955)Google Scholar
  8. 8.
    Buchholz, D.: Collision theory for massless Bosons. Commun. Math. Phys.52, 147–173 (1977)CrossRefGoogle Scholar
  9. 9.
    Buchholz, D.: On particles, infraparticles, and the problem of asymptotic completeness. In: VIIIth International Congress on Mathematical Physics, Marseille 1986. Singapore: World Scientific 1987Google Scholar
  10. 10.
    Buchholz, D., Stein, U.: In preparationGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Detlev Buchholz
    • 1
  1. 1.II. Institut für Theoretische PhysikUniversität HamburgHamburg 50Federal Republic of Germany

Personalised recommendations