New approach for calculating the dressed quark propagator at finite chemical potential

Abstract

A new method for obtaining the chemical potential dependence of the dressed quark propagator in the rainbow approximation of the Dyson-Schwinger equation is developed. In the above approximation we prove that the dressed quark propagator at finite chemical potential \ensuremath{\mu} can be written as ${\mathcal{G}}_{0}^{\ensuremath{-}1}[\ensuremath{\mu}]=i\ensuremath{\gamma}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{~}{p}A({\stackrel{~}{p}}^{2})+B({\stackrel{~}{p}}^{2})$ with ${\stackrel{~}{p}}_{\ensuremath{\mu}}=(\stackrel{\ensuremath{\rightarrow}}{p},{p}_{4}+i\ensuremath{\mu})$. From this the chemical potential dependence of the ``effective'' two-quark condensate is evaluated. A comparison with previous results is given.