ON THE NON-TRIVIALITY OF THE λφ⁴ MODEL

Abstract

The λφ4 model is conventionally used to explain the origin of mass of elementary particles through the Spontaneous Symmetry Breaking (SSB) phenomena. The triviality status of the λφ4 model in 4-dimensional spacetime remains an open question despite attempts by several authors. This study establishes a new approach to determine the triviality status of the λφ4 model based on an unpublished note by Professor Bryce DeWitt. We adopted the DeWitt's Ansatz for the 2-point connected correlation function on the lattice [Formula: see text] where α is a parameter that measures the departure from triviality. Calling α's continuum counterpart as β, then a non-zero value of β signifies non-triviality of the λφ4 model. The 2-point connected correlation function, given in terms of an Euclidean functional integral, is computed numerically via Monte Carlo methods. Our analysis, based on β, is different from the traditional analysis based on the renormalized coupling constant λR. To test the new approach, we performed the simulation in 2 dimensions and obtained results that are consistent with previous findings: 2-dimensional λφ4 model is non-trivial. Finally, for the case in 4 dimensions, our results show that the model is non-trivial.