p-Adic physics below and above Planck scales

TL;DR

This paper explores the application of p-adic numbers to pre-spacetime physics, proposing models that eliminate loop divergences and naturally incorporate the concept of mass through p-adic structures.

Contribution

It introduces a novel p-adic model based on R^n to Q_p extensions that avoids loop divergences and explains mass as an inverse transition probability.

Findings

p-adic models can eliminate loop divergences in quantum field theory

Mass arises naturally as inverse transition probability in p-adic models

New applications of p-adic numbers to pre-spacetime physics are proposed

Abstract

We present a rewiew and also new possible applications of $p$-adic numbers to pre-spacetime physics. It is shown that instead of the extension $R^n\to Q_p^n$, which is usually implied in $p$-adic quantum field theory, it is possible to build a model based on the $R^n\to Q_p$, where p=n+2 extension and get rid of loop divergences. It is also shown that the concept of mass naturally arises in $p$-adic models as inverse transition probability with a dimensional constant of proportionality.