Hard thermal loops and beyond in the finite temperature world-line formulation of QED - art. no. 125022

We derive the hard thermal loop action for soft electromagnetic fields in t he finite temperature world-line formulation at imaginary time by first int egrating out the hard fermion modes from the microscopic QED action. Furthe r, using the finite T world-line method, we calculate all static higher ord er terms in the soft electromagnetic field. At hi,oh T, the leading non-lin ear terms are independent of the temperature and, except for a term quartic in the time component of the vector potential, they cancel exactly against the vacuum contribution. The remaining T-dependent non-linear terms become more strongly suppressed by the temperature as the number of soft fields i ncreases, thus making the expansion reliable.