Microscopic identification of dissipative modes in relativistic field theories

william r. scott;

We present an argument to support the existence of dissipativemodes in relativistic field theories. For an O(N) ϕ4 theory in spatial dimension 1 ≤ d ≤ 3, the two-point function of ϕ is shown to develop a pole of the form p0 ∼ i −1(p2 + m2) at small energy p0 and momentum p, with a
nonzero finite coefficient or relaxation constant, ,when evaluated in the two-particle irreducible (2PI) framework at the next-leading order (NLO) of 1/N expansion. In contrast, an NLO calculation
in the one-particle irreducible (1PI) framework fails to give a nonzero . The dissipative mode emerges from multiple scattering of a particle with other particles, which is appropriately treated in the 2PI–NLO calculation through the resummation of secular terms to improve the
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.