Construction of p-adic Covariant Quantum Fields in the Framework of White Noise Analysis

TL;DR

This paper develops a framework for constructing interacting p-adic Euclidean quantum fields using white noise calculus, extending white noise analysis to p-adic spaces and ensuring they satisfy key axioms of quantum field theory.

Contribution

It introduces p-adic Kondratiev and Hida spaces for quantum field construction, a novel extension of white noise calculus to p-adic settings.

Findings

Constructed a large class of p-adic quantum fields

Fields satisfy Osterwalder-Schrader axioms except reflection positivity

Extended white noise calculus to p-adic spaces

Abstract

In this article we construct a large class of interacting Euclidean quantum field theories, over a p-adic space time, by using white noise calculus. We introduce p-adic versions of the Kondratiev and Hida spaces in order to use the Wick calculus on the Kondratiev spaces. The quantum fields introduced here fulfill all the Osterwalder-Schrader axioms, except the reflection positivity.