The Relativistic one dimensional Coulomb problem and Relativistic PIMC method

TL;DR

This paper investigates the relativistic one-dimensional Coulomb problem using the Path Integral Monte Carlo method, identifying critical coupling where bound states vanish, applicable across different regularizations and potentially testable experimentally.

Contribution

It introduces a novel application of the PIMC method to the relativistic Coulomb problem and determines the critical coupling for bound state disappearance.

Findings

Critical coupling law for bound state disappearance

Relativistic and non-relativistic regime analysis

Potential experimental testability of the law

Abstract

The Relativistic one dimensional Coulomb problem was studied by means of the Path Integral Monte Carlo method. Relativistic and non-relativistic regimes of this problem were investigated. The relativistic regime appears at small masses of the particle and (or) at strong coupling. Critical coupling at which the bound state disappears was founded. This law is valid for any finite regularization of the Coulomb potential and potentially can be tested experimentally.