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

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

2003-06-30

arxiv.org/abs/gr-qc/0306126v1

Annals Phys. 310 (2004) 95

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LateX, 10 pages

Scientific paper

10.1016/j.aop.2003.08.019

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.

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