Friedberg-Lee model at finite temperature and density

Abstract

The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant $B(T)$ and $B(T,\ensuremath{\mu})$ have been calculated at different temperatures and densities. It is shown that there is a critical temperature ${T}_{C}\ensuremath{\simeq}106.6$ MeV when $\ensuremath{\mu}=0$ MeV and a critical chemical potential $\ensuremath{\mu}\ensuremath{\simeq}223.1$ MeV for fixing the temperature at $T=50$ MeV. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T\ensuremath{\leqslant}{T}_{C}$ (or $\ensuremath{\mu}\ensuremath{\leqslant}{\ensuremath{\mu}}_{C}$), there is a bag constant $B(T)$ [or $B(T,\ensuremath{\mu})$] and the soliton solutions are stable. However, when $T>{T}_{C}$ (or $\ensuremath{\mu}>{\ensuremath{\mu}}_{C}$) the bag constant $B(T)=0$ MeV [or $B(T,\ensuremath{\mu})=0$ MeV] and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.