Electrostatic analogy of the Jackiw-Rebbi zero energy state

TL;DR

This paper draws an analogy between the Jackiw-Rebbi zero energy state in quantum field theory and a classical electrostatic problem, offering a new pedagogical perspective and a simplified implementation method.

Contribution

It introduces a novel electrostatic analogy for the Jackiw-Rebbi zero energy state, facilitating understanding and teaching of this quantum model through basic electrostatics.

Findings

Electrostatic analogy successfully models the zero energy state.

Inhomogeneous permittivity mimics the scalar potential.

Provides a simple electrostatic setup for the Jackiw-Rebbi model.

Abstract

We present an analogy between the one dimensional Poisson equation in inhomogeneous media and the Dirac equation in one space dimension with a Lorentz scalar potential for zero energy. We illustrate how the zero energy state in the Jackiw-Rebbi model can be implemented in a simple one dimensional electrostatic setting by using an inhomogeneous electric permittivity and an infinite charged sheet. Our approach provides a novel insight into the Jackiw-Rebbi zero energy state and provides a helpful view in teaching this important quantum field theory model using basic electrostatics.