The progress in the last decade in perturbative quantum field theory at high temperatures and densities, made possible by the use of effective field theories and hard thermal/dense loop resummations in ultrarelativistic gauge theories, is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far is given together with references to a few of the most recent developments and open problems.

https://iopscience.iop.org/article/10.1088/0034-4885/67/3/R05/pdf

Advances in perturbative thermal field theory

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.

We determine the damping rates of slow-moving photons in next-to-leading order hard-thermal-loop perturbation of massless QED. We find both longitudinal and transverse rates finite, positive, and equal at zero momentum. Various divergences, light-cone and at specific momenta, but not infrared, appear and cancel systematically.

Photon damping in one-loop HTL perturbation theory

The damping rate t (p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p 2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between t (0) and l (0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.

Infrared Behavior of High-Temperature QCD

The damping rate γt(p) of on-shell transverse gluons with ultrasoft momentum p is obtained in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature massless quantum chromodynamics (QCD). It is obtained in an expansion to the second order in p. The first coefficient known in the literature is recovered, but that of order p2 is found to be divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. By carrying out similar calculations in the context of scalar quantum electrodynamics, it is shown that early and late external-momentum expansions yield identical results.

Infrared behaviour of high-temperature quantum chromodynamics (QCD)

We determine the analytic expression of the damping rates for very soft moving quarks in an expansion to second order in powers of their momentum in the context of QCD at high temperature. The calculation is performed using the hard-thermal-loop-summed perturbation scheme. We describe the range of validity of the expansion and make a comparison with other calculations, particularly those using a magnetic mass as a shield from infrared sensitivity. We discuss the possible occurrence of infrared divergences in our results and argue that they are due to magnetic sensitivity.

Damping of very soft moving quarks in high-temperature QCD

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Damping of very soft moving quarks in high-temperature QCD

Damping of very soft moving quarks in high-temperature QCD