On Relativistic Irreducible Quantum Fields Fulfilling CCR

  • K. Baumann
Conference paper

Abstract

POWERS [1] has shown that in more than one space dimension all irreducible Fermi fields which fulfill CAR are necessarily free fields. Based on estimates given by HERBST [2] we shall show that irreducible Bose fields which fulfill CCR are free fields in d > 3 space dimensions. In d = 3 and d = 2 space dimensions CCR restricts the interaction to be renormalizable. The superrenormalizable models do fulfill CCR as we know from Constructive Quantum Field Theory.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.T. Powers: Absence of Interaction as a Consequence of Good Ultraviolett Behavior in the Case of a Local Fermi Field, Commun. Math. Phys. 4, 145–156 (1967)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    I.W. Herbst: On Canonical Quantum Field Theories, J. Math. Phys. 17, 1210–1221 (1976)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    K. Baumann: On Relativistic Irreducible Quantum Fields Fulfilling CCR, J. Math. Phys. 28 697–704 (1987)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • K. Baumann
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenFed. Rep. of Germany

Personalised recommendations