Hard thermal loops and beyond in the finite temperature world-line formulation of QED

Abstract

We derive the hard thermal loop action for soft electromagnetic fields in the finite temperature world-line formulation at imaginary time, by first integrating out the hard fermion modes from the microscopic QED action. Further, using the finite T world-line method, we calculate all static higher order terms in the soft electromagnetic field. At high T , the leading non-linear 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 increases, thus making the expansion reliable. Applications of this method to other theories and problems at the soft scale are also briefly discussed.

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

“…During the last two decades, these "string-inspired" representations have already found a considerable number of applications in QED, both for the calculation of photon amplitudes [8,14,23] and the effective action itself [24][25][26][27][28]. They have been generalised to include constant external fields [23,[29][30][31][32][33] as well as finite temperature [34][35][36][37][38][39]. Their…”

Dimensional regularization for the particle transition amplitude in curved space

“…For the case of worldline path integrals on the circle, i.e. with periodic boundary conditions, several applications soon followed these papers, ranging from multiloop calculations [6], finite temperature computations [7,8], the inclusion of constant external electromagnetic fields [9][10][11] and Heisenberg-Euler lagrangians [12], and many more. Worldline path integrals on the line were used instead to compute, for instance, thermal Green's functions [13], to represent scalar and Dirac propagators [14,15], as well as open line spin factors [16], and more recently in the worldgraph approach [17,18] and to obtain master formulas from the photon-dressed Dirac propagators [19]-see the review papers [20,21] for an extensive bibliography and a summary of classic and more recent applications.…”

Dimensional Regularization for the Particle Transition Amplitude in Curved Space

“…For the case of worldline path integrals on the circle, i.e. with periodic boundary conditions, several applications soon followed these papers, ranging from multiloop calculations [6], finite temperature computations [7,8], the inclusion of constant external electromagnetic fields [9][10][11] and Heisenberg-Euler lagrangians [12], and many more. Worldline path integrals on the line were used instead to compute, for instance, thermal Green's functions [13], to represent scalar and Dirac propagators [14,15], as well as open line spin factors [16], and more recently in the worldgraph approach [17,18] and to obtain master formulas from the photon-dressed Dirac propagators [19]-see the review papers [20,21] for an extensive bibliography and a summary of classic and more recent applications.…”