Derivation of Nonperturbative Relativistic Two-Body Equations from the Action Principle in Quantumelectrodynamics

Abstract

For two fermion fields Ψ1(x) and Ψ2(x) interacting with the electromagnetic field via the minimal and Pauli-couplings we introduce a composite field ϕ(x1, x2). The total action can be rewritten in terms of ϕ and its time derivatives if we use the physical retarded Green's functions Dret (corresponding to an effective to (1/2)(Dret + Dadv) = D) between two particles. The variation of the action with respect to ϕ gives then exact covariant two-body, one-time, equations with relativistic potentials. The center of motion can be covariantly separated leading to an infinite component wave equation for the composite system, which reduces to the well-known covariant wave equation for the moving H-atom in the limit m2 ∞.