  In the imaginay-time formalism of thermal field theory, and also in the
real-time formalism but by means of some redefined physical propagators for
scalar bound states by diagonalization of four-point function matrices, we
reexamine the Nambu-Goldstone mechanism of electroweak symmetry breaking in a
one-generation fermion condensate scheme, based on the Schwinger-Dyson equation
in the fermion bubble diagram approximation, and compare the obtained results.
We have reached the conclusion that in both the formalisms, the Goldstone
theorem of spontaneous electroweak symmetry breaking is rigorously true for the
case of mass-degenerate two flavors of fermions and only approximately valid at
low energy scales for the mass-nondegenerate case, in spite of existence of
some difference between the two formalisms in the imaginary parts of the
denominators of the propagators for scalar bound states. When the two flavors
of fermions have unequal nonzero masses, the induced possible fluctuation
effect for the Higgs particle is negligible if the momentum cut-off in the zero
temperature loops is large enough. All the results show physical equivalence of
the two formalisms in the present discussed problems.
