Canonical Approach to High-Energy Scattering in Massive Quantum Electrodynamics

By the canonical Hamiltonian approach to field theory, we have studied the very high-energy limit of massive quantum electrodynamics. We introduce a series of canonical transformations which bring the usual Hamiltonian of a neutral-vector-meson interaction with a conserved current to the effective Hamiltonian that operates at infinite energy. The result we obtain for the S-matrix operator is that it factorizes at very high energies: $S={S}₀[{U}^{{}}T(exp({-}i{∫}{{-}{∞}}^{{∞}}dt {H}ₛ(t)))U]$ where ${S}₀$ is the $S$ matrix for the hard-meson "core," first given by Cheng and Wu and by Chang and Ma: ${S}₀=exp({-}i{{g}²}{{(2{π})}²}{∫}{d}²k{{j}R({k}_{{⊥}}){j}L({-}{k}L)}{{{k}_{{⊥}}}²+{{μ}}²})$ and the second operator describes the contribution to scattering due to pionization effects. $U$ is the dressing operator which clothes the hard-meson "core" in a coherent state of virtual soft mesons, and the $T$ product is obviously the time-evolution operator for softmeson dynamics.