Random fields as solutions of the inhomogeneous quaternionic Cauchy-Riemann equation. I. Invariance and analytic continuation |
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| Authors: | S Albeverio K Iwata T Kolsrud |
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| Institution: | (1) Ruhr-Universität Bochum and SFB 237, Bochum-Essen-Düsseldorf, Federal Republic of Germany;(2) Kungliga Tekniska Högskolan, Stockholm, Sweden;(3) BiBo-S Research Centre, Universität Bielefeld, Federal Republic of Germany;(4) CERFIM, Locarno, Switzerland |
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| Abstract: | We consider random fieldsA satisfying the quaternionic Cauchy-Riemann equation A=F, whereF is white noise. Under appropriate conditions onF, A is invariant under the proper Euclidean group in four dimensions, but in general not under time reflection. The Schwinger functions can be analytically continued to Wightman functions satisfying the relativistic postulates on invariance, specrral property and locality. |
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