zbMATH — the first resource for mathematics

Axioms for Euclidean Green’s functions. II. (English) Zbl 0303.46034

46F05 Topological linear spaces of test functions, distributions and ultradistributions
46L05 General theory of \(C^*\)-algebras
46F10 Operations with distributions and generalized functions
Full Text: DOI
[1] Constantinescu, F., Thalheimer, W.: Euclidean Green’s functions for Jaffe fields. Commun. math. Phys.38, 299–316 (1974) · Zbl 0291.46029
[2] 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
[3] Fröhlich, J.: Schwinger functions and their generating functionals. Helv. Phys. Acta47, 265 (1974) · Zbl 0345.46057
[4] Gelfand, I.M., Shilov, G.E.: Generalized functions, Vol. II, p. 227. New York and London: Academic Press 1968 · Zbl 0177.36302
[5] Glaser, V.: The positivity condition in momentum space. In: Problems of theoretical physics. Moscow: Nauka 1969
[6] Glaser, V.: On the equivalence of the Euclidean and Wightman formulations of field theory. Commun. Math. Phys.37, 257 (1974) · Zbl 0295.46064
[7] Glimm, J., Jaffe, A.: A remark on the existence of 4 4 . Phys. Rev. Lett.33, 440–441 (1974) · Zbl 1329.81210
[8] Glimm, J., Jaffe, A., Spencer, T.: The Wightman axioms and particle structure in theP()2 quantum field model. Ann. Math.100, 585 (1974)
[9] Hörmander, L.: On the division of distributions by polynomials. Arkiv Mat.3, 555 (1958) · Zbl 0131.11903
[10] Mandelbrojt, S.: Séries adhérentes, régularisation des suites, applications. Paris: Gauthier-Villars 1952
[11] Nelson, E.: Construction of quantum fields from Markoff fields. J. Funct. Anal.12, 97 (1973) · Zbl 0252.60053
[12] Osterwalder, K., Schrader, R.: Axioms for Euclidean Green’s functions. Commun. math. Phys.31, 83 (1973) · Zbl 0274.46047
[13] 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 · Zbl 0335.46042
[14] Schwartz, L.: Théorie des distributions, p. 260. Paris: Hermann 1966
[15] Simon, B.: Positivity of the Hamiltonian semigroup and the construction of Euclidean region fields. Helv. Phys. Acta46, 686 (1973)
[16] Simon, B.: Private communication
[17] Simon, B.: Distributions and their hermite expansions. J. Math. Phys.12, 140 (1971) · Zbl 0205.12901
[18] Stein,M., Weiss,G.: Fourier analysis on Euclidean spaces, p. 38. Princeton University Press 1971 · Zbl 0232.42007
[19] Velo, G., Wightman, A.S. (Eds.): Constructive quantum field theory, Lecture notes in physics. Berlin-Heidelberg-New York: Springer 1973
[20] Vladimirov, V.S.: Methods of the theory of functions of several complex variables. Cambridge and London: MIT Press 1966
[21] Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63 (1934) · Zbl 0008.24902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.