Non-Archimedean White Noise, Pseudodifferential Stochastic Equations, and Massive Euclidean Fields

TL;DR

This paper constructs p-adic Euclidean random fields as solutions to stochastic pseudodifferential equations, introducing new mathematical frameworks and analyzing their invariance and Schwinger functions.

Contribution

It introduces a novel class of p-adic Euclidean fields, develops the associated nuclear Hilbert space framework, and studies their invariance properties and Schwinger functions.

Findings

Construction of p-adic Euclidean fields as solutions to stochastic equations

Introduction of nuclear countably Hilbert spaces for parameterizing fields

Analysis of invariance and Schwinger functions of the fields

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. 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}.