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The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proved to have the identical form in both the imaginary and the real time formalism of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyse the dependence on temperature T and chemical potential μ of the dynamical top-quark mass as the order parameter characteristic ofdoi:10.1088/0253-6102/32/3/425 fatcat:zo2ci5ginjhmjjr3dxhfqmkduu