Microscopic identification of dissipative modes in relativistic field theories
Progress of Theoretical and Experimental Physics
We present an argument to support the existence of dissipative modes in relativistic field theories. In an O(N) φ^4 theory in spatial dimension d< 3, a relaxation constant Γ of a two-point function in an infrared region is shown to be finite within the two-particle irreducible (2PI) framework at the next-leading order (NLO) of 1/N expansion. This immediately implies that a slow dissipative mode with a dispersion p_0∼ iΓ^2 is microscopically identified in the two-point function. Contrary, NLO
... n. Contrary, NLO calculation in the one-particle irreducible (1PI) framework fails to yield a finite relaxation constant. Comparing the results in 1PI and 2PI frameworks, one concludes that dissipation emerges from multiple scattering of a particle with a heat bath, which is appropriately treated in the 2PI-NLO calculation through the resummation of secular terms to improve long-time behavior of the two-point function. Assuming that this slow dissipative mode survives at the critical point, one can identify the dynamic critical exponent z for the two-point function as z=2-η. We also discuss possible improvement of the result.