Abstract
We consider a boson field φ(x) under an interaction of the form ∫V(φ k (x))dx, where φ k (x) is the momentum cut-off field, andV(α) is a continuous bounded function. Under a weak regularity condition onV(α), we prove that the total energy operator is self adjoint, that the asymptotic fields exist and that the scattering operator exists.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Friedrichs, K. O.: Perturbation of spectra in Hilbert space. Providence: Am. Math. Soc. 1965.
Glimm, J.: Boson fields with nonlinear selfinteraction in two dimensions. Commun. Math. Phys.8 12–25 (1968).
Glimm, J., andA. Jaffe: A: λφ4: quantum field theory without cut-offs. To appear.
Jaffe, A., O. Lanford, andA. S. Wightman: A general class of cut-off model fields. Preprint.
Höegh-Krohn, R.: Asymptotic limits in some models of quantum field theory I. J. Math. Phys. Jan. (1969).
-- Asymptotic limits in some models of quantum field theory II. J. Math. Phys. April (1969).
-- Asymptotic limits in some models of quantum field theory III. J. Math. Phys. To appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Höegh-Krohn, R. Boson fields under a general class of cut-off interactions. Commun.Math. Phys. 12, 216–225 (1969). https://doi.org/10.1007/BF01661576
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01661576