Multiple solutions of the self-consistency condition in the Walecka model and the validity of the Brown-Rho scaling law - art. no. 051302

We investigate the self-consistency condition (SCC) of mean-field theory in the Walecka model and find that the solutions of the SCC are multiple at h igh temperature and chemical potential. Using the effective Lagrangian appr oach, we study medium effects on the omega meson mass by taking into accoun t vacuum effects. We show that the omega meson mass decreases with both tem perature and chemical potential with a general tendency, while near the cri tical point several omega meson masses degenerate due to the multiple solut ions of the SCC. We check the validity of the Brown-Rho scaling law in this case. Finally, we calculate the thermodynamic potential and prove that the multiple solutions of the SCC result from a first-order phase transition o f nuclear matter in the Walecka model at high temperature and chemical pote ntial.