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

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 addi…