The dispersive effects of vacuum polarization on the propagation of a strong circularly polarized electromagnetic wave through a cold collisional plasma are studied analytically. It is found that, due to the singular dielectric features of the plasma, the vacuum effects on the wave propagation in a plasma are qualitatively different and much larger than those in pure vacuum in the regime when the frequency of the propagating wave approaches the plasma frequency. A possible experimental setup to detect these effects in plasma is described.
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The previous considerations hold at zero chemical potential. The effects of the chemical potential are more difficult to estimate because there are no expressions available for the two-loop effective Lagrangian at finite temperature and finite chemical potential. In this case, we proceed by estimating the chemical potential as that of an ideal gas, (Ref. 47). At the densities we will be interested in and at temperatures such that with in the optical regime [see the conditions below Eq. (11) on the laser frequency] then and it is sensible to assume that as for the temperature also the effects of the chemical potential can be neglected.
Since we are also considering the VPEs perturbatively up to first order in it would be more correct to also set . Nevertheless, the VPEs do not affect the zero-order Lorentz factors that are the only dynamical quantities entering the collision frequency because .