ON THE LOW-ENERGY SPECTRUM OF SPONTANEOUSLY BROKEN Φ4 THEORIES

The low-energy spectrum of a one-component, spontaneously broken 40 theory is generally believed to have the same simple massive form root p(2) + m(h)(2), as in the symmetric phase where <Phi > = 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 El (p) in the broken phase. This analytic result, while providing the trend E-1 (p) similar to root p(2) + m(h)(2) at large vertical bar p vertical bar, gives an energy gap E-1(0) < m(h), even when approaching the infinite-cutoff limit A -> infinity with that infinitesimal coupling lambda similar to 1/In A 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.