In a one-generation fermion condensate scheme of electroweak symmetry breaking, it is proved based on the Schwinger-Dyson equation in real-time thermal field theory in the fermion bubble diagram approximation that, at finite temperature T below the symmetry restoration temperature $T_c,$ a massive Higgs boson and three massless Nambu-Goldstone bosons could emerge from spontaneous breaking of the electroweak group ${\mathrm{SU}}_L\mathrm{}\left(2\right)\mathrm{}\times {\mathrm{U}}_Y\mathrm{}\left(1\right)\mathrm{}\to {\mathrm{U}}_Q\mathrm{}\left(1\right)\mathrm{}$ if the two fermion flavors in the one generation are mass degenerate; thus, the Goldstone theorem is rigorously valid in this case. However, if the two fermion flavors have unequal masses, owing to “thermal fluctuation,” the Goldstone theorem will be true only approximately for a very large momentum cutoff $\Lambda$ in the zero temperature fermion loop or for low energy scales. All possible pinch singularities are proved to cancel each other, as expected in a real-time thermal field theory.

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