Critical Behavior of Plasmon Damping Rate in Thermal Scalar Field

Abstract：

Thermal Renormalization Group equations are derived in the framework of Closed-Time-Path formalism in real-time temperature field theory. The numerical solutions of the Thermal Renormalization Group equations show that the coupling constant runs with temperature. Applying Thermal Renormalization Group equations to φ⁴ theory with spontaneously breaking symmetry, we investigate the critical behavior of the damping rate of the plasmon with finite momentum at the phase transition temperature of restoring symmetry. As the critical point is approached, it turns out that for the plasmon with finite momentum the damping rate decrease to zero. The tendence is opposite to that obtained by taking the no-runing coupling constant. The result is consistent with critical slowing down law.