In the collision of a high-energy proton beam and a strong laser field, merging of laser photons can occur due to the polarization of vacuum. The probability of photon merging is calculated by exactly accounting for the laser field which involves a highly nonperturbative dependence on the laser intensity and frequency. It is shown that the nonperturbative vacuum-polarization effects can be experimentally measured by combining the next generation of tabletop petawatt lasers with proton accelerators presently available.
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Piazza et al. (2008) studied this question.
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