p-Adic Dirac Equations and the Jackiw-Rebbi Model

TL;DR

This paper introduces a p-adic version of the Jackiw-Rebbi model, replacing real space with p-adic numbers, resulting in a non-local Hamiltonian that admits localized wavefunctions and models non-local interactions.

Contribution

The paper develops a novel p-adic formulation of the Jackiw-Rebbi model, incorporating non-local operators on p-adic fields, which was not previously explored.

Findings

The p-adic model admits localized wavefunctions.

The model allows for long-range, non-local interactions.

It reproduces the predictions of the standard model.

Abstract

We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on complex-valued functions defined on Q_{p}. These Hamiltonians admit localized wavefunctions and allow long-range interactions, so spooky action at a distance is allowed. These features are not present in the original model. The new model gives the same predictions as the standard one. The p-adic line serves as a discrete model for the physical space; in this type of space, non-locality emerges naturally.