Rigorous quantum field theory functional integrals over the p-adics: research announcement

TL;DR

This paper constructs scale-invariant non-Gaussian stochastic processes over three-dimensional p-adic space, confirming a long-standing prediction of anomalous dimensions and demonstrating a form of universality in quantum field theory.

Contribution

It rigorously constructs non-Gaussian p-adic quantum field models with anomalous dimensions, confirming predictions by Wilson and establishing universality properties.

Findings

Squared field has a dynamically generated anomalous dimension.

Construction confirms a prediction made over forty years ago.

Establishes a mild form of universality for the model.

Abstract

In this short note we announce the construction of scale invariant non-Gaussian generalized stochastic processes over three dimensional p-adic space. The construction includes that of the associated squared field and our result shows this squared field has a dynamically generated anomalous dimension which rigorously confirms a prediction made more than forty years ago, in an essentially identical situation, by Kenneth G. Wilson. We also prove a mild form of universality for the model under consideration.