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I ran into the following article by Varma, Higgs Boson in Superconductors
http://arxiv.org/abs/cond-mat/0109409
Varma compares the Gross-Pitaevskii equation with the Higgs Lagrangian and calculates the elementary excitations. He shows that although symmetry is broken in both cases, Higgs type excitations are absent in the G-P equation although it looks very similar to the Higgs equation, the main difference being that the former is only first order in t.
He then shows why in Superconductors one nevertheless obtains Higgs type excitations which he identified in experimental spectra together with Littlewood in 1982.
It is interesting how easily -at least my- intuition gets lost in QFT.
http://arxiv.org/abs/cond-mat/0109409
Varma compares the Gross-Pitaevskii equation with the Higgs Lagrangian and calculates the elementary excitations. He shows that although symmetry is broken in both cases, Higgs type excitations are absent in the G-P equation although it looks very similar to the Higgs equation, the main difference being that the former is only first order in t.
He then shows why in Superconductors one nevertheless obtains Higgs type excitations which he identified in experimental spectra together with Littlewood in 1982.
It is interesting how easily -at least my- intuition gets lost in QFT.