Abstract
We study the effect of the charge in the scattering of ultra high energetic particles. The ultrarelativistic limit of the boosted Reissner-Nordstrom geometry is found. This is a shock wave space-time in the limit when v→c and the mass and charge vanish as m=γ−1p and e=γ−1/2pe respectively, with p and pe being constants. (γ=(1−ν2)−1/2). The kinetic (p) and electromagnetic (pe) momenta of the particle contribute with different ρ-dependence [Formula: see text]. For pe=0, it gives the known Aichelburg-Sexl geometry. We find the exact S-matrix describing the scattering of a neutral massive test particle with this geometry, which generalizes the pe=0 result. This is an infinite superposition of the S-matrices for pe=0 and exhibits poles in both positive and negative axis Gs=im/2, (m∈Z). This increases the number of poles of the uncharged case by a factor of four. The large and small (s, t) behaviors are computed. The scattering in which the two particles are charged is highly complicated and not exactly solvable.
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