Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-01-11
Phys.Rev.D59:065007,1999
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, revtex, no figure, Phys. Rev. D, to appear
Scientific paper
10.1103/PhysRevD.59.065007
In a one-generation fermion condensate scheme of electroweak symmetry breaking, it is proven based on Schwinger-Dyson equation in the 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 the spontaneous breaking of electroweak group $SU_L(2)\times U_Y(1) \to U_Q(1)$ if the two fermion flavors in the one generation are mass-degenerate, thus Goldstone Theorem is rigorously valid in this case. However, if the two fermion flavors have unequal masses, owing to "thermal flactuation", the Goldstone Theorem will be true only approximately for a very large momentum cut-off $\Lambda$ in zero temperature fermion loop or for low energy scales. All possible pinch singularities are proven to cancel each other, as is expected in a real-time thermal field theory.
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