Two mechanisms for the elimination of pinch singularities in out of equilibrium thermal field theories

Abstract

We analyze ill-defined pinch singularities characteristic of out of equilibrium thermal field theories. We identify two mechanisms that eliminate pinching even at the single self-energy insertion approximation to the propagator: the first is based on the vanishing of phase space at the singular point ͑threshold effect͒. It is effective in QED with a massive electron and a massless photon. In massless QCD, this mechanism fails, but the pinches cancel owing to the second mechanism, i.e., owing to the spinor or tensor structure of the single self-energy insertion contribution to the propagator. The constraints imposed on distribution functions are very reasonable. ͓S0556-2821͑99͒02812-X͔

Out of equilibrium thermal field theories: Finite time after switching on the interaction and Wigner transforms of projected functions

“…Now, it is G R,∞ (p 0 , p) as given in Eq. (1.8) (and similar expressions for the advanced and Keldysh components and the single self-energy insertion approximation to G R(A,K),∞ ) to which previous results on the cancellation of pinching singularities [18,19,21,23] and the HTL resummation [27,28] (and also on the cancellation of collinear [16,17] and infrared singularities if the properties (1) and (2) hold at the two-loop level) apply.…”

“…(II. [23][24][25] in [23]. After taking into account that the product of the retarded with the advanced function, with the same time variables, vanishes, one obtains 16) where D and S are bare scalar propagators,…”

“…The Wigner transform over the infinite x 0 −y 0 interval gives as usual [4,12,15] (note, however, that we avoid [23] using the nonanalytic function ǫ(p 0 ) in the expression for G K,∞ ):…”

“…The pinchlike contribution to the Keldysh component of the resummed propagator is expressed as [23] (we treat only the scalar case) the diagrams with respect to the question of energy nonconservation. Indeed, we find that this feature appears together with the non-WTPF contributions.…”

“…A recent approach based on first principles has been successful in demonstrating the cancellation of collinear [16,17] and pinching singularities [18,19,20,21,22,23], the extension of the hard thermal loop (HTL) approximation [24,25,26] to out of equilibrium [27,28], and applications to heavy-ion collisions [29,30,31]. A weak point of the approach was that most of these results were obtained under the assumption that the variation of slow Wigner variables could be ignored or, in other words, that these results were valid only in the lowest order of the gradient expansion [32,33,34].…”