Interparticle Interactions and Nonlocality in Quantum Field Theory

Abstract

We consider a reformulation of quantum electrodynamics (and of field theories of a similar structure) in which covariant Green functions are used to solve for the mediating (electromagnetic) field in terms of the particle fields. The resulting Hamiltonian of the theory has an explicitly nonlocal interaction term in which the propagator of the mediating field appears directly. We discuss some advantages of this explicitly nonlocal formulation. In particular, we show that exact few-fermion eigenstates of the Hamiltonian can be obtained for a reduced model in the canonical equal-time formalism. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. In the simpler case where the particle and mediating fields are both scalar, the two body equation has analytic solutions for massless mediating fields.