Abstract
We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Constantinescu, F., Thalheimer, W.: Euclidean Green's functions for Jaffe fields. Commun. math. Phys.38, 299–316 (1974)
Epstein, H.: Some analytic properties of scattering amplitudes in quantum field theory. In: Chretien, M., Deser, S. (Eds.): Brandeis lectures 1965, Vol. I. New York: Gordon and Breach 1966
Fröhlich, J.: Schwinger functions and their generating functionals. Helv. Phys. Acta47, 265 (1974)
Gelfand, I.M., Shilov, G.E.: Generalized functions, Vol. II, p. 227. New York and London: Academic Press 1968
Glaser, V.: The positivity condition in momentum space. In: Problems of theoretical physics. Moscow: Nauka 1969
Glaser, V.: On the equivalence of the Euclidean and Wightman formulations of field theory. Commun. Math. Phys.37, 257 (1974)
Glimm, J., Jaffe, A.: A remark on the existence of ϕ 44 . Phys. Rev. Lett.33, 440–441 (1974)
Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in theP(ϕ)2 quantum field model. Ann. Math.100, 585 (1974)
Hörmander, L.: On the division of distributions by polynomials. Arkiv Mat.3, 555 (1958)
Mandelbrojt, S.: Séries adhérentes, régularisation des suites, applications. Paris: Gauthier-Villars 1952
Nelson, E.: Construction of quantum fields from Markoff fields. J. Funct. Anal.12, 97 (1973)
Osterwalder, K., Schrader, R.: Axioms for Euclidean Green's functions. Commun. math. Phys.31, 83 (1973)
Osterwalder, K.: Euclidean Green's functions and Wightman distributions. In: Velo, G., Wightman, A.S. (Eds.): Constructive quantum field theory, Lecture notes in physics. Berlin-Heidelberg-New York: Springer 1973
Schwartz, L.: Théorie des distributions, p. 260. Paris: Hermann 1966
Simon, B.: Positivity of the Hamiltonian semigroup and the construction of Euclidean region fields. Helv. Phys. Acta46, 686 (1973)
Simon, B.: Private communication
Simon, B.: Distributions and their hermite expansions. J. Math. Phys.12, 140 (1971)
Stein,M., Weiss,G.: Fourier analysis on Euclidean spaces, p. 38. Princeton University Press 1971
Velo, G., Wightman, A.S. (Eds.): Constructive quantum field theory, Lecture notes in physics. Berlin-Heidelberg-New York: Springer 1973
Vladimirov, V.S.: Methods of the theory of functions of several complex variables. Cambridge and London: MIT Press 1966
Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63 (1934)
Author information
Authors and Affiliations
Additional information
Communicated by A. S. Wightman
with an Appendix by Stephen Summers
Supported in part by the National Science Foundation under Grant MPS 73-05037 A01.
Alfred P. Sloan Foundation Fellow.
Rights and permissions
About this article
Cite this article
Osterwalder, K., Schrader, R. Axioms for Euclidean Green's functions II. Commun.Math. Phys. 42, 281–305 (1975). https://doi.org/10.1007/BF01608978
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01608978