Exact solutions of Dirac equation on a 2D gravitational background

TL;DR

This paper derives exact solutions for the Dirac equation on specific 2D curved spacetimes using supersymmetric quantum mechanics, providing explicit wave functions and spectra especially for a modified harmonic oscillator case.

Contribution

It introduces a method to solve the Dirac equation exactly on 2D gravitational backgrounds via supersymmetry, including explicit solutions for a modified harmonic oscillator.

Findings

Explicit wave functions for Dirac equation on 2D backgrounds

Energy spectra derived for specific curved spacetimes

Demonstrates supersymmetry as a tool for exact solvability

Abstract

We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified supersymmetric harmonic oscillator the wave function and energy spectrum of Dirac equation is given explicitly.