Physics – Mathematical Physics
Scientific paper
2004-09-21
Rev.Math.Phys. 8 (1996) 763-817
Physics
Mathematical Physics
69 pages, 1 figure
Scientific paper
We construct Euclidean random fields $X$ over $\R^d$, by convoluting generalized white noise $F$ with some integral kernels $G$, as $X=G* F$. We study properties of Schwinger (or moment) functions of $X$. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields. We present a partial negative result on the reflection positivity of convoluted generalized white noise. Furthermore, by representing the kernels $G_\a$ of the pseudo--differential operators $(-\D + m^2_0)^{-\alpha}$ for $\alpha \in (0,1)$ and $m_0>0$ as Laplace transforms we perform the analytic continuation of the (truncated) Schwinger functions of $X=G_\alpha * F$, obtaining the corresponding (truncated) Wightman distributions on Minkowski space which satisfy the relativistic postulates on invariance, spectral property, locality and cluster property. Finally we give some remarks on scattering theory for these models.
Albeverio Sergio
Gottschalk Hanno
Wu Jian-Liang
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