Exact two-body eigenstates in scalar quantum field theory

Exact few-particle eigenstates in partially reduced QED

“…This approach was then applied to two-body eigenstates in the scalar Yukawa (Wick-Cutkosky) theory [2,3]. We implement such an approach to QED in this paper.…”

“…The corresponding Euler-Lagrange equations of motion are the coupled Dirac-Maxwell equations, ( i γ µ ∂ µ − m 1 )ψ(x) = q 1 γ µ A µ (x)ψ(x), (1)(2) ( i γ µ ∂ µ − m 2 )φ(x) = q 2 γ µ A µ (x)φ(x), (1)(2)(3) and…”

“…The equations (1-2) -(1-4) can be decoupled in part by using the well-known [4,5] formal solution of the Maxwell equation (1)(2)(3)(4), namely 6) where D µν (x − x ′ ) is a Green function (or photon propagator in QFT terminology), defined by…”

“…and A 0 µ (x) is a solution of the homogeneous (or "free field") equation (1)(2)(3)(4) with j µ (x) = 0. We recall, in passing, that equation (1-7) does not define the covariant Green function D µν (x − x ′ ) uniquely.…”

“…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).…”