Two-fermion Dirac-like eigenstates of the Coulomb QED Hamiltonian

Exact few-particle eigenstates in partially reduced QED

“…In the rest frame of the three-body system equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) reduces to one in two independent vectors only. Nevertheless, the reduction of the equation for states of given J P is more formidable than in the two-body case.…”

“…If we had used the Lorentz-gauge form of the Green function (2-5), equation (3)(4)(5)(6)(7)(8)(9)(10)(11) would take on the form (4)(5)(6) which is recognized to be the Eddington-Gaunt equation [20,21]. The Gaunt equation, unlike the Breit equation, does not contain even lowest-order retardation effects (see, also, section 5, following).…”

“…To our knowledge no exact (analytic or numeric) solutions of equations (1)(2)(3)(4)(5)(6)(7)(8) and (1)(2)(3)(4)(5)(6)(7)(8)(9) for classical fields have been reported in the literature, even for the case of a single fermion field (say φ = 0), though approximate (perturbative) solutions have been discussed by various authors, particularly Barut and his coworkers (see refs. [6,7] and citations therein).…”

“…The partially reduced equations (1)(2)(3)(4)(5)(6)(7)(8)- (1)(2)(3)(4)(5)(6)(7)(8)(9) are derivable from the stationary action principle…”

“…( [1][2][3][4][5][6][7][8][9][10][11][12] One can proceed to do conventional covariant perturbation theory using the reformulated QED Lagrangian (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11). The interaction part of (1-11) has a somewhat modified structure from that of the usual formulation of QED.…”