Magnetic field and curvature effects on pair production. I. Scalars and spinors

The pair production rates for spin-0 and $\mathrm{spin}\text{−}\frac{1}{2}$ particles are calculated on spaces of the form $M\times {\mathbb{R}}^{1,1}$, with $M$ corresponding to ${\mathbb{R}}^2$ (flat); $T^2$ (flat, compactified); $S^2$ (positive curvature); and $H^2$ (negative curvature), with and without a background magnetic field on $M$. The motivation is to elucidate the effects of the curvature and background magnetic field. Contrasting effects for positive and negative curvature on the two cases of spin are obtained. For positive curvature, we find enhancement for spin-0 and suppression for $\mathrm{spin}\text{−}\frac{1}{2}$, with the opposite effect for negative curvature.

Figure 1

$\gamma (\omega )$ vs $\omega$ on $T^2\times {\mathbb{R}}^{1,1}$.

Figure 2

${\gamma }_0(\omega )$ vs $\omega$.

Figure 3

${\gamma }_0(\omega )$ vs $\omega$.

Figure 4

${\gamma }_{1/2}$ vs $\omega$.

Figure 5

${\gamma }_0(\omega )$ vs $\omega$.

Figure 6

${\gamma }_0(\omega )$ vs $\omega$.

Figure 7

Comparison of ${\gamma }_0$ at zero magnetic field for the torus, sphere, and hyperboloid.

Figure 8

${\gamma }_{1/2}$ vs $\omega$.

Figure 9

${\gamma }_{1/2}$ vs $\omega$.

Figure 10

Comparison of ${\gamma }_{1/2}$ at zero magnetic field for the torus, sphere, and hyperboloid.