Abstract
This note presents a construction of generalized random fields (prop. 1 and 2). In particular if we base our construction on a given Euclidean invariant field, the new one will have the same invariance. Similarly the properties of T-positivity and clustering carry over to the new models. A Gaussian input will give rise to non-Gaussian fields such as e.g. the “ultralocal” ones.
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References
I.M. Gelfand, N.Ya. Vilenkin: Generalized Functions, vol. 4, Applications of Harmonic Analysis. Acad.Press, New York (1964), Ch.II § 2.1.
B. Simon: The P((P)2 Euclidean (Quantum) Field Theory. Princeton University Press (1976) § VIII.3
J. Fröhlich: Helv. Phys. Acta 47, 265 (1974)
J. Klauder: Functional Techniques and their Application in Quantum Field Theory. In Lectures in Theoretical Physics vol. XIV (Boulder 1973)
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© 1979 Springer-Verlag
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Gielerak, R., Karwowski, W., Streit, L. (1979). Construction of a class of characteristic functionals. In: Albeverio, S., et al. Feynman Path Integrals. Lecture Notes in Physics, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09532-2_73
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DOI: https://doi.org/10.1007/3-540-09532-2_73
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