Particle content of the Gaussian functional approximation to the scalar φ4 theory

The particle content of the Gaussian functional approximation to the φ4 theory with a spontaneously broken O(2) symmetry is investigated in view of apparent existence of two kinds of particles with quantum numbers of the Goldstone boson: a massive “elementary” and a massless Goldstone “composite” particle. We calculate the Källén-Lehmann spectral functions of the two-point Green functions in the Gaussian approximation. The massive particle is absent from the spectral function in the “pion” channel. Similar results hold in the “sigma” channel, our treatment of which is novel.