NONPERTURBATIVE N-POINT FUNCTIONS FROM THE GAUSSIAN EFFECTIVE ACTION AND RENORMALIZATION OF LAMBDA-PHI-4

Recently, a covariant variational approach was developed to obtain a class of lower-bound approximations to GAMMA(1PI), the generating functional of one-particle irreducible graphs. The gaussian effective action (GEA) emerged in this context as a natural lower-bound to GAMMA(1PI). In this letter we renormalize the GEA, applying a scheme suggested by Consoli, based on the background field method. The renormalized GEA seems to indicate that, although SSB occurs, the shifted theory is free - as found by Consoli in a RG analysis of the effective potential. However, a functional expansion of the shifted GEA, involving the n-point functions, suggests that the particles of the theory are also massless.