Abstract
A mistake in the paper [1] on the “Axioms for Euclidean Green's Functions” is corrected in the following sense: thanks to these axioms the Euclidean Schwinger functionsS n can be analytically continued to the corresponding Wightman functionsW n possessing all the correct analyticity properties and satisfying a generalized positivity condition in the complex domain. It is however suggested by the proof that their tempered behaviour near the Minkowski points cannot be guaranteed without additional assumptions.
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Osterwalder, K., Schrader, R.: Commun. math. Phys.31, 83–112 (1973)
Glaser, V.: Problems of theoretical physics, p. 69. Moscow: “Nauka” 1969
Jost, R.: The general theory of quantized fields. Amer. Math. Soc. Publ., Providence (1965)
Epstein, H.: Axiomatic field theory, Vol. 1, p. 3. New York: Gordon and Breach Publ., 1966
Epstein, H., Glaser, V., Martin, A.: Commun. math. Phys.13, 257–316 (1969)
Zerner, M.: Les fonctions holomorphes à valeurs vectorielles et leurs valeurs aux bords, mimeographed notes of a series of lectures. Orsay (1961)
Osterwalder, K.: Lecture notes in physics, Vol. 25, pp. 71–93. Berlin-Heidelberg-New York: Springer 1973
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Communicated by A. S. Wightman
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Glaser, V. On the equivalence of the Euclidean and Wightman formulation of field theory. Commun.Math. Phys. 37, 257–272 (1974). https://doi.org/10.1007/BF01645941
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DOI: https://doi.org/10.1007/BF01645941