COVARIANT SINGLE-TIME BOUND-STATE EQUATION

Abstract

We derive a system of covariant single-time equations for a two-body bound state in a model of scalar fields $ϕ_1$ and $ϕ_2$ interacting via exchange of another scalar field $χ$. The derivation of the system of equations follows from the Haag expansion. The equations are linear integral equations that are explicitly symmetric in the masses, $m_1$ and $m_2$, of the scalar fields, $ϕ_1$ and $ϕ_2$. We present an approximate analytic formula for the mass eigenvalue of the ground state and give numerical results for the amplitudes for a choice of constituent and exchanged particle masses.