We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. A simple Fock-space variational trial state is used to derive relativistic two-fermion wave equations variationally. We require the trial state to be an eigenstate of the square of the total relativistic angular momentum operator,its projection and parity. It is shown that, in the case of different masses of the particle and the antiparticle, a mixing of single and triplet states takes place. For small coupling constants the fine structure is calculated analytically up to fourth order for all states and mass ratios.
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