Euclidean Quantum Field Formulation of p-Adic open string amplitudes

TL;DR

This paper develops a rigorous mathematical framework for p-adic quantum field theories, expressing N-point amplitudes as series involving Igusa's local zeta functions, with the lowest term relating to p-adic open string amplitudes.

Contribution

It introduces a novel series expansion for p-adic quantum field theory amplitudes using Igusa's local zeta functions, connecting to p-adic string theory.

Findings

Amplitudes can be expressed as a series of Igusa's local zeta functions.

The lowest term corresponds to a regularized p-adic open string amplitude.

Provides a rigorous mathematical foundation for p-adic quantum field theories.

Abstract

We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.