Introduction to theN-Quantum Approximation for Bound States: the Deuteron in Pseudoscalar-Meson Theory

Abstract

The $N$-quantum approximation for bound states in relativistic quantum field theory is described by applying it to the deuteron in pseudoscalar-meson theory. Some properties of the covariant, single-time, $N$-quantum amplitude which plays the role of the deuteron wave function are given. A manifestly covariant single-time equation for this amplitude is derived. In the weak-binding, nonrelativistic limit, this equation is reduced to a Pauli-Schrödinger equation with the correct reduced mass and the usual second-order perturbation-theory central and tensor potentials. The interpretation of the $N$-quantum bound-state amplitude in the weak-binding, nonrelativistic limit is discussed. It is pointed out that a higher approximation will lead to a short-range force between nucleons.