Abstract
We propose a constructive approach to φ 44 . It is based on formulating the φ 44 theory as an implicit function problem using multiplicative renormalization. For the corresponding lattice formulation we reduce the problem to verifying three conjectures. One conjecture is a regularity condition. The remaining two concern properties of the classical Ising ferromagnet, one of which we discuss in the frame work of critical point analysis.
Similar content being viewed by others
References
Baker, G.A., Jr.: Selfinteracting boson quantum field theory and the thermodynamic limit ind dimensions. J. Math. Phys.16, 1324–1346 (1975)
Bjoerken, J., Drell, S.: Relativistic quantum fields. New York: McGraw Hill 1965
Bröcker, Th., Jänich, K.: private communication
Buckingham, M.J., Gunton, J.D.: Correlations at the critical point in the Ising model. Phys. Rev.178, 848–853 (1969)
Domb, C.: The Ising model. In: Phase transitions and critical phenomena. Vol. 3 (eds. C. Domb, M.S. Green). London, New York: Academic Press 1974
Fisher, M.E.: Rigorous inequalities for critical point correlation exponents. Phys. Rev.180, 594–600 (1974)
Gallavotti, G., Martin-Löf, A.: Block-spin distributions of short range attractive Ising models. N.C.25, 425–441 (1975)
Glimm, J., Jaffe, A.: A remark on the existence of φ 44 . Phys. Rev. Letters33, 440–441 (1974)
Glimm, J., Jaffe, A.: Absolute bounds on vertices and couplings. Ann. Inst. H. Poincaré22 (1975)
Glimm, J., Jaffe, A.: Critical problems in quantum fields. Talk presented at the international colloquim on mathematical methods of quantum field theory. Marseille 1975, to appear
Guelfand, I.M., Vilenkin, N.Y.: Les distributions,TIV. Paris: Dunod 1967
Guerra, F., Robinson, D.W., Stora, R., eds.: International colloquium on mathematical methods of quantum field theory. Marseille 1975, to appear
Guerra, F., Rosen, L., Simon, B.: TheP(φ)2 euclidean quantum field theory as classical statistical mechanics. Ann. Math.101, 111–259 (1975)
Hepp, K.: Proof of the Bogoliubov Parasiuk theorem on renormalization. Commun. math. Phys.2, 301–326 (1966)
Isaacson, D.: The critical behaviour of the anharmonic oszillator. Rutgers University preprint 1975
Karowski, M., Meyer, S.: private communication
Newman, C.: Inqualities for Ising models and field theories which obey the Lee-Yang theorem. Commun. math. Phys.41, 1–9 (1975)
Osterwalder, K., Schrader, R.: Axioms for euclidean green's functions, I and II. Commun. math. Phys.31, 83–112 (1973);42, 281–305 (1975)
Rosen, J.: Mass renormalization of the λφ4 euclidean lattice field theory. New York: Rockefeller University preprint 1975
Schrader, R.: New rigorous inequality for critical exponents in the Ising model. Berlin preprint 1975
Schrader, R.: A possible constructive approach to φ 44 II. Berlin University preprint 1976
Simon, B.: TheP(φ)2 euclidean quantum field theory. Princeton Series in Physics. Princeton: Princeton University Press 1974
Wilson, K.G., Kogut, J.: The renormalization group and the ε expansion. Phys. Rep.12, 75–200 (1975)
Zimmermann, W.: Local operator products and renormalization. In: Lectures on elementary particles and quantum field theory (eds. Deser, Grisaru, Pendleton). Cambridge: MIT Press 1970
Author information
Authors and Affiliations
Additional information
Communicated by A. S. Wightman
Rights and permissions
About this article
Cite this article
Schrader, R. A possible constructive approach to φ 44 . Commun.Math. Phys. 49, 131–153 (1976). https://doi.org/10.1007/BF01608737
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01608737