An asymptotics theorem for low-energy compton scattering in the degenerate case

Abstract

This representation exhibits explicitly the Lorentz and gauge invariance of the S-matrix. The invariant amplitudes A and B describe the photon–target interaction dynamics. In what follows, k and k′ (p and p′) are the photon (target) initial and finite pulses, P = 1/2(p + p′), χ = 1/4(s− u), s and u are the Mandelstam variables, and eμ is the photon polarization vector. In what follows, we use the Coulomb gauge and the laboratory system of coordinates and consider scattering in the lowest perturbation order. For simplicity, we neglect higher-order effects, in particular, infrared divergences, whose contribution to the particle structure parameters was studied earlier in [2]. The low-energy theorems [3]–[6] state that, up to ω2 (ω = k0), the amplitude T can be represented as T = e ∗ e ′(αω2 − 2e) + ( e× k)( e ′ × k′) β, (1)