Spin 0 and spin 1/2 particles in a constant scalar-curvature background

TL;DR

This paper solves the Klein-Gordon and Dirac equations in a curved spacetime with constant scalar curvature, revealing the energy spectra and transverse momentum constraints for spin-0 and spin-1/2 particles.

Contribution

It provides exact solutions for scalar and spinor particles in a specific curved background and compares their energy eigenvalues, highlighting differences in their ground state properties.

Findings

Both particles require nonzero transverse momentum.

Bosons have a minimum energy E_min, while fermions do not.

Exact eigenfunctions and energy spectra are obtained.

Abstract

We study the Klein-Gordon and Dirac equations in the presence of a background metric ds^2 = -dt^2 + dx^2 + e^{-2gx}(dy^2 + dz^2) in a semi-infinite lab (x>0). This metric has a constant scalar curvature R=6g^2 and is produced by a perfect fluid with equation of state p=-\rho /3. The eigenfunctions of spin-0 and spin-1/2 particles are obtained exactly, and the quantized energy eigenvalues are compared. It is shown that both of these particles must have nonzero transverse momentum in this background. We show that there is a minimum energy E^2_{min}=m^2c^4 + g^2c^2\hbar^2$ for bosons E_{KG} > E_{min}, while the fermions have no specific ground state E_{Dirac}>mc^2.