Quark condensate at finite baryon density

We discuss a recently derived, model-independent relation that expresses the value of a medium-modified quark condensate in terms of the vacuum value of the condensate and the value of the nucleon sigma term, ${\mathrm{\sigma }}_{\mathit{N}}$. Our goal is to calculate the value of the quark condensate in nuclear matter, 〈NM‖q¯(0)q(0)‖NM〉, using some standard many-body techniques. Here, we comment on the mean-field calculations of Cohen, Furnstahl, and Griegel and others. We then calculate the value of the nuclear matter quark condensate using linear response theory. In a sigma-dominance model, the linear response calculation relates the modification of the vacuum condensate to the matrix element of the operator q¯q taken between a state of the sigma meson and the vacuum. (That matrix element may be used to define a sigma decay constant, ${\mathit{f}}_{\mathrm{\sigma }}$.) We also provide some additional insight into the relation between the dynamics of the quark condensate and the scalar fields of relativistic nuclear physics.