## International Conference on $p$-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS $p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

Wilson A. Zuniga-Galindo

### Non-Archimedean White Noise, Massive Euclidean Fields, and Schwinger Functions

Abstract

We construct $p$-adic Euclidean random fields $\Phi$ over $Q_{p}^{N}$, for arbitrary $N$, these fields are solutions of $p$-adic stochastic pseudodifferential equations of Klein-Gordon type. From a mathematical perspective, the Euclidean fields are generalized stochastic processes parametrized by functions belonging to a nuclear countably Hilbert space, these spaces are introduced in this article, in addition, the Euclidean fields are invariant under the action of certain group of transformations. We also study the Schwinger functions of $\Phi$. arXiv:1501.00707 .