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. © 1979 Springer-Verlag.