Magnetic field and curvature effects on pair production. II. Vectors and implications for chromodynamics

We calculate the pair production rates for spin-1 or vector particles on spaces of the form $M\times {\mathbb{R}}^{1,1}$, with $M$ corresponding to ${\mathbb{R}}^2$ (flat), $S^2$ (positive curvature), and $H^2$ (negative curvature), with and without a background (chromo)magnetic field on $M$. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for $S^2$ and $H^2$ is obtained. We also give a brief discussion of how our results relate to ideas about confinement in non-Abelian theories.

Figure 1

The graph of $f_1(x)$ showing enhancement due to the background magnetic field.

Figure 2

Cutoff $m^2{a}^2=4$.

Figure 3

No cutoff, $m^2{a}^2=0$.

Figure 4

${\gamma }_1(\omega )$ at $b=0$.

Figure 5

${\gamma }_1(\omega )$ at $0<b<\frac{1}{2}$ and no infrared cutoff.

Figure 6

${\gamma }_1(\omega )$ at $\frac{1}{2}<b<\frac{3}{2}$ and no infrared cutoff.

Figure 7

${\gamma }_1(\omega )$ at $b>\frac{3}{2}$ and infrared cutoff value $m^2{a}^2=8$.

Figure 8

${\gamma }_1(\omega )$ at $b>\frac{3}{2}$ and no infrared cutoff.

Figure 9

Comparison of ${\gamma }_1$ at zero magnetic field for the sphere and hyperboloid.