Debye mass in the accelerating frame

We consider a conformal scalar field theory with the $\lambda \phi^4$ self-coupling in Rindler and Minkowski coordinates at a finite-temperature with the Planckian distribution for exact modes. The solution of the one-loop Dyson–Schwinger equation is found through the order $\lambda^{3/2}$. The appearance of a thermal (Debye) mass is shown. Unlike the physical mass, the thermal mass gives a gap in the energy spectrum in the quantization in the Rindler coordinates. The difference between such calculations in Minkowski and Rindler coordinates for exact modes is discussed. It is also shown that states with a temperature lower than the Unruh temperature are unstable. It is proved that for the canonical Unruh temperature, the thermal mass is equal to zero. The contribution to the quantum average of the stress–energy tensor is also calculated, it remains traceless even in the presence of the thermal mass.