Quasifermion spectrum at finite temperature from coupled Schwinger-Dyson equations for a fermion-boson system

We nonperturbatively investigate a fermion spectrum at finite temperature in a chiral invariant linear sigma model. Coupled Schwinger-Dyson equations for fermion and boson are developed in the real time formalism and solved numerically. From the coupling of a massless fermion with a massive boson, the fermion spectrum shows a three-peak structure at some temperatures even for the strong coupling region. This means that the three-peak structure which was originally found in the one-loop calculation is stable against higher order corrections even in the strong coupling region.

Figure 1

Self-energies for fermion (left) and boson (right). Solid lines denote the fermion propagator and dashed lines the boson propagator.

Figure 2

The fermion spectral functions ${\rho }_{+}m$ for $g^2=1$ and $T/m=0.6$ (top left), 0.8 (top middle), 1.0 (top right), 1.2 (bottom left), 1.6 (bottom middle), 2.0 (bottom right). The figure is clipped at ${\rho }_{+}m=50$.

Figure 3

Temperature-dependence of the fermion spectral function ${\rho }_{+}m$ for $p=0$, $g^2=1$.

Figure 4

The fermion self-energy ${\Sigma }_{+}/m$ for $p=0$, $g^2=1$: the imaginary part (left panel) and the real part (right panel).

Figure 5

The kinetic processes by the Landau damping contained in the imaginary part of the fermion self-energy at one loop. (The corresponding inverse processes are not shown.) The solid line represents the fermion and the dashed one the on-shell boson with the energy $E_{p-k}=\sqrt{(\mathbf{p}-\mathbf{k}{)}^2+m^2}$. The fermion with the energy $k$ is also on-shell.

Figure 6

The spectral functions ${\rho }_{+}(p_0,0)m$ for $g^2=1$ and $T/m=0.6$, 1.2, 1.6, 2 from top to bottom.

Figure 7

The fermion spectral functions ${\rho }_{+}m$ for $T/m=1$ and $g^2=0.4$ (left), 2 (middle), 4 (right). The figure is clipped at ${\rho }_{+}m=50$.

Figure 8

The imaginary part of the fermion self-energy ${\Sigma }_{+}/m$ for $p=0$, $T/m=1$.

Figure 9

The spectral functions ${\rho }_{+}(p_0,0)m$ for $T/m=1$ and $g^2=1$, 2, 4 from top to bottom.

Figure 10

The peak position of the normal quasifermion for $p=0$ and $T/m=1$.