Zero energy states of Dirac equation in $(2+1)$-dimensional curved spacetime

TL;DR

This paper investigates zero energy solutions of the Dirac equation in a (2+1)-dimensional curved spacetime with scalar potential, revealing conditions for degeneracy related to momentum, mass, and potential coupling.

Contribution

It provides a novel analysis of zero energy states in curved spacetime, deriving specific conditions for degeneracy involving momentum and scalar potential parameters.

Findings

Zero energy states are degenerate under certain conditions.

Solutions depend on constraints involving momentum, mass, and scalar potential.

Degeneracy occurs when specific relations between parameters are satisfied.

Abstract

We consider Dirac equation in $(2+1)$ dimensional curved spacetime in the presence of a scalar potential. It is then shown that the zero energy states are degenerate and they can be obtained when the momentum $k_y$ in the $y$ direction satisfies certain constraints involving the mass parameter and the scalar potential coupling.