A gap-less mode of the singlet Higgs field

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Recent lattice results suggest the existence of a gap-less mode of the singlet Higgs field. We present a description of spontaneous symmetry breaking in $λΦ^4$ theories showing why one is faced with long-wavelength, collective modes of the scalar condensate with $\tilde{E}({\bf{p}}) \to 0$ energy in the ${\bf{p}} \to 0$ limit.
10 pages

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