Skip to main content
SpringerLink
Log in

Phase transitions for φ 42 quantum fields

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

Abstract

Phase transitions for the quantum field interaction λφ4+m 20 φ2,m 20 /λ≪1 are established in two dimensional space time.

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

References

  1. Dobrushyn, R., Minlos, R.: Construction of a one-dimensional quantum field via a continuous Markov field. Funct. Anal. Appl.7, 324–325 (1973)

    Google Scholar 

  2. Fröhlich, J.: Schwinger functions and their generating functionals. II. Adv. Math. (to appear)

  3. Glimm, J., Jaffe, A.: The λ(φ4)2 quantum field theory without cutoffs. IV. J. Math. Phys.13, 1558–1584 (1972).

    Google Scholar 

  4. Glimm, J., Jaffe, A.: On the approach to the critical point. Ann. Inst. Henri Poincaré22, 13–26 (1975)

    Google Scholar 

  5. Glimm, J., Jaffe, A.: φj bounds inP(φ)2 quantum field models. Proc. of the Colloq. on Math. Methods of Quantum Field Theory, Marseille, June 1975

  6. Glimm, J., Jaffe, A.: Two and three body equations in quantum field models. Commun. math. Phys.44, 293–320 (1975)

    Google Scholar 

  7. Glimm, J., Jaffe, A., Spencer, T.: A cluster expansion for the φ 42 quantum field theory in the two phase region (in preparation)

  8. Guerra, F., Rosen, L., Simon, B.: Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2. Commun. math. Phys.27, 10–22 (1972)

    Google Scholar 

  9. Guerra, F., Rosen, L., Simon, B.: The vacuum energy forP(φ)2 infinite volume limit and coupling constant dependence. Commun. math. Phys.29, 233–247 (1973)

    Google Scholar 

  10. Guerra, F., Rosen, L., Simon, B.: TheP(φ)2 Euclidean quantum field theory as classical statistical mechanics. Ann. Math.101, 111–259 (1975)

    Google Scholar 

  11. Pirogov, S. A., Sinai, Ya. G.: Phase transitions of the first kind for small perturbations of the Ising model. Funct. Anal. Appl.8, 21–25 (1974) (Engl. trans.)

    Google Scholar 

  12. Simon, B., Griffiths, R.: The φ 42 field theory as a classical Ising model. Commun. math. Phys.33, 145–164 (1973)

    Google Scholar 

  13. Glimm, J., Jaffe, A., Spencer, T.: Existence of phase transitions for φ 42 quantum fields. Proc. of the Colloq. on Math. Methods of Quantum Field Theory, Marseille, June 1975

Download references

Author information

Authors and Affiliations

  1. Rockefeller University, 10021, New York, N.Y., USA

    James Glimm

  2. Harvard University, 02138, Cambridge, Mass., USA

    Arthur Jaffe & Thomas Spencer

Authors
  1. James Glimm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arthur Jaffe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Spencer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by K. Hepp

Supported in part by the National Science Foundation under Grant MPS 74-13252.

Supported in part by the National Science Foundation under Grant MPS 73-05037.

On leave from Rockefeller University, New York, NY 10021, USA.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glimm, J., Jaffe, A. & Spencer, T. Phase transitions for φ 42 quantum fields. Commun.Math. Phys. 45, 203–216 (1975). https://doi.org/10.1007/BF01608328

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01608328

Keywords

Search

Navigation