ON THE LOW-ENERGY SPECTRUM OF SPONTANEOUSLY BROKEN Φ4THEORIES

Abstract

The low-energy spectrum of a one-component, spontaneously broken Φ4theory is generally believed to have the same simple massive form [Formula: see text] as in the symmetric phase where 〈Φ〉 = 0. However, in lattice simulations of the 4D Ising limit of the theory, the two-point connected correlator and the connected scalar propagator show deviations from a standard massive behavior that do not exist in the symmetric phase. As a support for this observed discrepancy, we present a variational, analytic calculation of the energy spectrum E1(p) in the broken phase. This analytic result, while providing the trend [Formula: see text] at large |p|, gives an energy gap E1(0)< mh, even when approaching the infinite-cutoff limit Λ→∞ with that infinitesimal coupling λ ~ 1/ ln Λ suggested by the standard interpretation of "triviality" within leading-order perturbation theory. We also compare with other approaches and discuss the more general implications of the result.