Quantum transport and the phase space structure of the Wightman functions

Abstract

We study the phase space structure of exact quantum Wightman functions in spatially homogeneous, temporally varying systems. In addition to the usual mass shells, the Wightman functions display additional coherence shells around zero frequency k 0 = 0, which carry the information of the local quantum coherence of particle-antiparticle pairs. We find also other structures, which encode non-local correlations in time, and discuss their role and decoherence. We give a simple derivation of the cQPA formalism, a set of quantum transport equations, that can be used to study interacting systems including the local quantum coherence. We compute quantum currents created by a temporal change in a particle's mass, comparing the exact Wightman function approach, the cQPA and the semiclassical methods. We find that the semiclassical approximation, which is fully encompassed by the cQPA, works surprisingly well even for very sharp temporal features. This is encouraging for the application of semiclassical methods in electroweak baryogenesis with strong phase transitions.

Electroweak baryogenesis at high bubble wall velocities

“…There has been a long-standing divide among practitioners of electroweak baryogenesis as to which transport equations to use; yet no systematic comparison between them has been made in the literature. We undertake to do so in this section, continuing with the ansatz for the wall profiles and spatially varying top quark mass (48,50) introduced previously.…”

“…Second, it has been derived both using WKBmethods [28,36,37] and from the fundamental CTPformalism [29][30][31][32]. Third, the semiclassical limit has been recently shown to arise in a full quantum mechanical treatment without any gradient expansion [50] (for earlier related work see [51] and [52][53][54][55][56][57][58]. ).…”

Flavour mixing transport theory and resonant leptogenesis

“…Dissipation shows up as a finite width of the pole functions in the Wigner representation. Going to the Wigner representation, finding quasiparticle poles and computing the corresponding quasiparticle widths γ k , and transforming back to the two-time representation, one could then obtain a more general A k effecting an explicit non-unitary decay of correlations in the relative time [79]:…”

“…Our formalism is a generalisation of the coherent quasiparticle approximation (cQPA) first developed in [72][73][74][75][76][77][78] and further studied in [79]. The cQPA is a two-step approximation where the structure of the Wightman function is solved first in a collisionless approximation in the Wigner representation.…”

Analytic techniques for solving the transport equations in electroweak baryogenesis

“…In this paper, we work strictly in the perturbative approach. Recent results and reviews that are relevant to the semiclassical approach can be found in [23][24][25] and references therein.…”