THE CURVED SHOCK WAVE SPACE-TIME OF ULTRARELATIVISTIC CHARGED PARTICLES AND THEIR SCATTERING

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.