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Hegerfeldt, Gerhard C.

Extremal decomposition of Wightman functions and of states on nuclear \(^*\)-algebras by Choquet theory. (English) Zbl 0315.46064

Commun. Math. Phys. 45, 133-135 (1975).
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Cited in 18 Documents

MSC:

46N99 Miscellaneous applications of functional analysis
46H99 Topological algebras, normed rings and algebras, Banach algebras
46K99 Topological (rings and) algebras with an involution
46A40 Ordered topological linear spaces, vector lattices
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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[2] Borchers, H. J., Yngvason, J.: Integral representations for Schwinger functionals and the moment problem over nuclear spaces. Commun. math. Phys.43, 255–271 (1975) · Zbl 0307.46054 · doi:10.1007/BF02345023
[3] Choquet, G.: Lectures on analysis. Vol. II. Ed. Marsden, J., Lance, T., Gelbart, S. New York: Benjamin 1969 · Zbl 0181.39602
[4] Dixmier, J.: LesC*-algèbres et leurs représentations. Paris: Gauthiers-Villars 1964
[5] Gelfand, I. M., Vilenkin, N. Ya.: Generalized functions, Vol. 4. New York: Academic Press 1964 (Remark after Theorem 1 in Chapter I, § 4.4)
[6] Hegerfeldt, G. C.: Decomposition into irreducible representations for the canonical commutation relations. Nuovo CimentoB4, 225–244 (1971)
[7] Hegerfeldt, G. C.: On canonical commutation relations and infinite-dimensional measures. J. Math. Phys.13, 45–50 (1972) · Zbl 0232.46040 · doi:10.1063/1.1665849
[8] Maurin, K.: General eigenfunction expansions and unitary representations of topological groups. Warszawa: Polish Scientific Publishers 1968 (p. 83) · Zbl 0185.39001
[9] Pietsch, A.: Nuclear locally convex spaces. Berlin-Heidelberg-New York: Springer 1972. Chapter 4.4.1/9 · Zbl 0308.47024
[10] Haviland, E. K.: On the moment problem for distribution functions in more than one dimension, I. Am. J. Math.57, 562–568 (1935) · Zbl 0013.05904 · doi:10.2307/2371187
[11] Kolmogoroff, A.: Grundbegriffe der Wahrscheinlichkeitsrechnung. Ergeb. Math.2, 27–30 (1933) · JFM 59.1152.03
[12] Araki, H.: Hamiltonian formalism and the canonical commutation relations in quantum field theory. J. Math. Phys.1, 492–504 (1960) (Theorems 10.1/2) · Zbl 0099.22906 · doi:10.1063/1.1703685
[13] Wyss, W.: On Wightman’s theory of quantized fields. In: Lectures in theoretical Physics. Boulder 1968. New York: Gordon and Breach 1969
[14] Challifour, J. L., Sklinker, S. P.: Euclidean Field Theory I. The Moment Problem. Commun. math. Phys.43, 41 (1975) · Zbl 0317.46059 · doi:10.1007/BF01609140
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