PHYSICAL MECHANISMS GENERATING SPONTANEOUS SYMMETRY BREAKING AND A HIERARCHY OF SCALES

We discuss the phase transition in (3+1)-dimensional λΦ⁴ theory from a very physical perspective. The particles of the symmetric phase ("phions") interact via a hard-core repulsion and an induced, long-range -1/r³ attraction. If the phion mass is sufficiently small, the lowest-energy state is not the "empty" state with no phions, but is a state with a nonzero density of phions Bose–Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with <Φ> ≠ 0 and its excitations ("phonons" in atomic physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m² passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M_h. This interesting physics coexists with "triviality;" all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio , which goes to zero in the continuum limit, can be viewed as a measure of nonlocality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.