Self-field QED(1+1) with massless matter fields: Two-body problem
  We consider two-body problem in the self-field (1+1)-dimensional quantum electrodynamics on the circle. We present two formulations of the problem which correspond to two different types of variational principles and prove that both formulations lead to the same spectrum of the two-body Hamiltonian with massless matter fields. We give the exact and complete solution of the relativistic two-body equation in the massless case. 
Fuad M. Saradzhev