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Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption ofthe analytieity of the fermion-boson vertex in the neighborhood of zero chemical potential(μ=0)and neglecting theμ-dependence of the dressed gluon propagator,we apply the method in[Phys.Rev.C 71(2005)015205]of studyingthe dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ canalso be obtained from the one at μ=0 by a simple shift of variables.Using this result we extend the results of[Phys.Lett.B 420(1998)267]to the situation of finite ehemical potential and show that under the approximations we havetaken,the Ge11-Mann Oakes Renner relation also holds at finite chemical potential.
Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analytieity of the fermion-boson vertex in the neighborhood of zero chemical potential (μ = 0) and neglecting the μ-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 (2005) 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ canalso be obtained from the one at μ = 0 by a simple shift of variables.Using this result we extend the results of [Phys. Lett. B 420 (1998) 267] to the situation of finite ehemical potential and show that under the approximations we havetaken, the Ge11-Mann Oakes Renner relation also holds at finite chemical potential.