Spontaneous symmetry breaking and the $p\to 0$ limit

Abstract

We point out a basic ambiguity in the $p\to 0$ limit of the connected propagator in a spontaneously broken phase. This may represent an indication that the conventional singlet Higgs boson, rather than being a purely massive field, might have a gap-less branch. This would dominate the energy spectrum for $\mathbf{p}\to 0$ and give rise to a very weak, long-range force. The natural interpretation is in terms of density fluctuations of the `Higgs condensate': in the region of very long wavelengths, infinitely larger than the Fermi scale, it cannot be treated as a purely classical c-number field.

17 pages, LaTex, small changes and some comments added

References in corpus (3)

• Reentrant violation of special relativity in the low-energy corner
• Long-wavelength excitations of Higgs condensates
• Lattice measurement of the energy-gap in a spontaneously broken phase

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