A Krein Quantization Approach to Klein Paradox

TL;DR

This paper applies Krein quantization to the Klein paradox, demonstrating that considering negative modes resolves the paradox and yields accurate current densities.

Contribution

It introduces a Krein quantization method to address the Klein paradox, providing a novel approach to eliminate the paradoxical behavior.

Findings

Exact current densities obtained without paradox

Negative modes are crucial in the quantization process

Krein approach resolves Klein paradox issues

Abstract

In this paper we first introduce the famous Klein paradox. Afterwards by proposing the Krein quantization approach and taking the negative modes into account, we will show that the expected and exact current densities, could be achieved without confronting any paradox.