The resummation of one particle lines

We propose a partial resummation for a weak coupling cluster expansion. The resummation gives one particle lines with in/out field propagators. We give a Bethe-Salpeter equation in which one particle subtractions are defined using physical one particle states. By these methods, we show that P(φ)₂ quantum fields in the weak coupling region have only isolated bound state spectrum below the 2 m threshold. Here P is not restricted to be even.