Skip to main content
SpringerLink
Log in

Boson fields with the :Φ4: Interaction in three dimensions

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The :Φ4: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized HamiltonianH ren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in whichH ren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliography

  1. Friedrichs, K.: Perturbation of spectra in Hilbert space. Providence: Am. Math. Soc. 1965.

    Google Scholar 

  2. Glimm, J.: Yukawa coupling of quantum fields in two dimensions, I. Commun. Math. Phys.5, 343–386 (1967).

    Google Scholar 

  3. —— Yukawa coupling of quantum fields in two dimensions, II. Commun. Math. Phys.6, 61–76 (1967).

    Google Scholar 

  4. —— Boson fields with nonlinear selfinteraction in two dimensions. Commun. Math. Phys.8, 12–25 (1968).

    Google Scholar 

  5. —, andA. Jaffe: A Yukawa interaction in infinite volume. Commun. Math. Phys. To appear.

  6. Jaffe, A.: Wick polynomials at a fixed time. J. Math. Phys.7, 1250–1255 (1966).

    Google Scholar 

  7. ——, andR. Powers: Infinite volume limit of a Φ4 field theory. Commun. Math. Phys.7, 218–221 (1968).

    Google Scholar 

  8. Nelson, E.: A quartic interaction in two dimensions. In: Mathematical theory of elementary particles, ed. byR. Goodman, andI. Segal, pp. 69–73. Cambridge: M.I.T. Press 1966.

    Google Scholar 

  9. Kristensen, P., L. Mejlbo, andE. Poulsen: Tempered distributions in infinitely many dimensions II. Math. Scand.14, 129–150 (1964).

    Google Scholar 

  10. —— —— ——: Tempered distributions in infinitely many dimensions. III. Commun. Math. Phys.6, 29–48 (1967).

    Google Scholar 

  11. Symanzik, K.: Euclidean quantum field theory I. J. Math. Phys.7, 510–525 (1966).

    Google Scholar 

  12. Wightman, A.: Introduction to some aspects of the relativistic dynamics of quantized fields. Institute des Hautes Etudes Scientifiques, Bures-sur-Yvette (Revised notes for lectures at the French summer school of theoretical physics, Cargese, Corsica, July 1964).

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Mass.

    James Glimm

Authors
  1. James Glimm
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the National Science Foundation, NSF GP 7477.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glimm, J. Boson fields with the :Φ4: Interaction in three dimensions. Commun.Math. Phys. 10, 1–47 (1968). https://doi.org/10.1007/BF01654131

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01654131

Keywords

Search

Navigation