Strictly finite range forces from the signum-Gordon field: exact results in two spatial dimensions

TL;DR

This paper derives an exact formula for the force between two static charges in a two-dimensional nonlinear scalar field model, revealing that the force vanishes beyond a critical separation distance.

Contribution

It provides the first exact solution for the force in the two-dimensional signum-Gordon model, including a critical distance where the force disappears.

Findings

Force between charges is exactly calculated.

Force vanishes beyond a critical separation.

Solution expressed as a one-dimensional integral.

Abstract

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between the charges exceeds certain critical value.