Abstract
We prove a number of asymptotic results in theP(φ)2 theory in the limit when the space cut-offs are removed, in particular the behavior ofE l andZ t,l ast,l→∞. Such results are used to study the question of orthogonality of infinite volume Euclidean measuresμ ∞(λ) for varying interaction constants λ.
Similar content being viewed by others
References
Glimm, J., Jaffe, A.: Boson quantum field models. In: Mathematics of Contemporacy Physics (R. Streater, Ed.). New York: Academic Press 1972
Guerra, F., Rosen, L., Simon, B.: Commun. math. Phys.27, 10–22 (1972)
Guerra, F., Rosen, L., Simon, B.: TheP(φ)2 Euclidean quantum field theory as classical statistical mechanics: Ann. Math. (to appear)
Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in theP(φ)2 quantum field model: Ann. Math. (to appear)
Newman, C.M.: J. Funct. Anal.14, 44–61 (1973)
See, for example, Blum, J.R., Hanson, D.L.: Pacific J. Math.10, 1125–1130 (1960), Corollary 2
Fröhlich, J.: Verification of axioms for Euclidean and relativistic fields and Haag's theorem in a class ofP(φ)2 models: Harvard University preprint (1974)
Simon, B.: Private communication
Dimock, J.: Perturbation expansion for theP(φ)2 Schwinger functions. In: Constructive Quantum Field Theory (G. Velo, A.S. Wightman Eds.). Berlin-Heidelberg-New York: Springer 1973
Schrader, R.: On the Euclidean version of Haag's theorem inP(ϕ)2 Theories. Commun. math. Phys.36, 133–136 (1974) Erratum: Commun. math. Phys.38, 81–82 (1974)
Guerra, F., Rosen, L., Simon, B.: Commun. math. Phys.29, 233–247 (1973)
Brody, E.J.: Z. Wahrscheinlichkeitstheorie20, 217–226 (1971)
Author information
Authors and Affiliations
Additional information
Communicated by A. S. Wightman
Rights and permissions
About this article
Cite this article
Lenard, A., Newman, C.M. Infinite volume asymptotics inP(ø)2 field theory. Commun.Math. Phys. 39, 243–250 (1974). https://doi.org/10.1007/BF01614243
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01614243