Pair production in a plane wave by thermal background photons

Ever since Schwinger published his influential paper [J. Schwinger, Phys. Rev. 82, 664 (1951)], the maxim that there can be no pair creation in a plane wave has been often cited. We advance an analysis that indicates that in any real situation, where thermal effects are present, in a single plane-wave field, even in the limit of zero frequency (a constant crossed field), thermal photons can seed pair creation. Interestingly, the pair-production rate is found to depend nonperturbatively on both the amplitude of the constant crossed field and on the temperature.

Figure 1

The envisaged scenario of thermal photons (wavy lines) interacting via the polarization operator (thick circles) in equilibrium with an intense external constant crossed field $(\mathit{E},\mathit{B})$ (thicker gray lines, indicating the direction $\mathit{\varkappa }=\mathit{E}\times \mathit{B}/EB$).

Figure 2

Logarithm of the expected number of pairs generated in a constant crossed field in the tiny space-time volume ${ƛ}^4=7.4\times {10}^{-53}{\mathrm{cm}}^3\mathrm{s}$. The area above the solid line signifies where the background process of pair creation due to purely thermal effects [see Eq. (1)] is at least 10% of that due to the external field interacting with the thermal photon gas [see Eq. (8)]. Above the dashed line, the number of pairs created in a typical strong optical laser four-volume ${\Omega }_l=6\times {10}^{-26}{\mathrm{cm}}^3\mathrm{s}$ is larger than unity.

Figure 3

Relative difference $|\Delta {\rho }_{\mathrm{th}}(T,{\chi }_E)|/{\rho }_{\mathrm{th}}(T,{\chi }_E)$ between the exact and asymptotic formulas for the thermal density of created pairs [using Eq. (2) in Eq. (4) and using Eq. (8), respectively], plotted as a function of $\delta$.