Quasisecular Perturbative Method for Calculating Bound States in Quantum Field Theory

A calculational procedure is given for determining bound states in quantum field theory using an approximation to the field determined from the equations of motion by the method of quasisecular perturbation theory. The method is illustrated using the ${\phi }^4$ model of quantum field theory. Although the procedure is based on a perturbation theory, it leads to binding energies which are nonanalytic in the coupling constant. The bound state occurs for arbitrarily weak coupling in the cases of one and two space dimensions, but not for three. Comparison is made with the Bethe-Salpeter equation in the ladder approximation. The result agrees for one dimension, but differs for two and three.