Skip to main content
Log in

Scalar Quantum Electrodynamics on the lattice as classical statistical mechanics

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

Abstract

Wilson's lattice approximation allows us to apply classical statistical mechanics ideas to the study of Scalar Quantum Electrodynamics. Our main tools are Griffiths-Kelly-Sherman inequalities, the transfer matrix formalism and exponential bounds. Our main result is the existence of the infinite volume limit for every value of the coupling parameters.

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

Access this article

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. Balian, R., Drouffe, J. M., Itzykson, C.: Phys. Rev. D10, 3376–3395 (1974)

    Google Scholar 

  2. De Angelis, G. F., de Falco, D.: Lettere Nuovo Cimento18, 536–538 (1977)

    Google Scholar 

  3. Fröhlich, J.: Phase transitions, goldstone bosons, and topological superselection rules. Proceedings of the Internationale Universitätswochen für Kernphysik, Schladmig, February 1976

  4. Ginibre, J.: Commun. Math. Phys.16, 310–328 (1970)

    Google Scholar 

  5. Glimm, J., Jaffe, A., Spencer, T.: The particle structure of the weakly coupledP(φ)2 model and other applications of high temperature expansions. In: Constructive quantum field theory (ed. G. Velo, A.S. Wightman) Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  6. Glimm, J., Jaffe, A.: Phys. Letters66 B 67–69 (1977)

    Google Scholar 

  7. Glimm, J., Jaffe, A.: Instantons in aU(1) lattice gauge theory: a coulomb dipole gas. Preprint (1977)

  8. Gohberg, I. C., Krein, M. G.: Introduction to the theory of nonselfadjoint operators. Providence: American Mathematical Society 1969

    Google Scholar 

  9. Guerra, F., Rosen, L., Simon, B.: Ann. Math.101, 111–259 (1975)

    Google Scholar 

  10. Kogut, J. B.: Three lectures on lattice gauge theory. Lecture series presented at the International Summer Institute for Theoretical Physics. Bielefeld August 1976

  11. Lüscher, M.: Construction of a selfadjoint strictly positive transfer matrix for Euclidean lattice gauge theories. Preprint (1976)

  12. Lüscher, M.: Absence of spontaneous gauge symmetry breaking in Hamiltonian lattice gauge theories. Preprint (1977)

  13. Nelson, E.: Probability theory and Euclidean field theory. In: Constructive quantum field theory (ed. G. Velo, A.S. Wightman). Berlin-Heidelberg-New York: 1973

  14. Osterwalder, K.: Gauge theories on the lattice. Lecture delivered at the 1976 Cargèse Summer School. Preprint (1976)

  15. Osterwald, K., Seiler, E.: Gauge field theories on the lattice. Preprint (1977)

  16. Polyakov, A. M.: Nucl. Phys. B120, 429–458 (1977)

    Google Scholar 

  17. Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton: Princeton University Press 1974

    Google Scholar 

  18. Wilson, K. G.: Phys. Rev. D10, 2445–2459 (1974)

    Google Scholar 

  19. Yang, C. N., Mills, R. L.: Phys. Rev.96, 191 (1954)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Angelis, G.F., de Falco, D. & Guerra, F. Scalar Quantum Electrodynamics on the lattice as classical statistical mechanics. Commun.Math. Phys. 57, 201–212 (1977). https://doi.org/10.1007/BF01614162

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01614162

Keywords

Navigation