Abstract
The hard thermal loop (HTL) effective field theory of QED can be derived from the classical limit of transport theory, corresponding to the leading term in a gradient expansion of the quantum approach. In this paper, we show that power corrections to the HTL effective Lagrangian of QED can also be obtained from transport theory by including higher orders in such gradient expansion. The gradient expansion is increasingly infrared (IR) divergent, but the correction that we compute is IR finite. We employ dimensional regularization, and show that this result comes after a cancellation of divergencies between the vacuum and medium contributions. While the transport framework is an effective field theory of the long distance physics of the plasma, we show that it correctly reproduces the correct QED ultraviolet divergencies associated with the photon wave function renormalization.
Highlights
The characterization of relativistic hot plasmas is an extensive field of investigation which has applications ranging from nuclear physics to condensed matter and cosmology
It is possible to show that the physics of the soft scales can be studied within this framework, reproducing the hard thermal loops (HTL) Feynman diagrams [13,14,15,16,17]
We will not address this issue here. While it is well-known that the HTL effective Lagrangian can be derived from the classical limit of transport theory, in this work we have shown how the power corrections to the HTL can be reproduced within this approach, by keeping next-to-leading order terms of the gradient expansion
Summary
The characterization of relativistic hot plasmas is an extensive field of investigation which has applications ranging from nuclear physics to condensed matter and cosmology. It is possible to show that the physics of the soft scales can be studied within this framework, reproducing the HTL Feynman diagrams [13,14,15,16,17] This effective approach has been used successfully to study numerically the dynamical evolution of relativistic plasmas, as lattice techniques are in principle only amenable to study their thermodynamics. Over the past few years, a renewed interest in the role of quantum effects in transport theory has been motivated by the study of chiral plasmas, characterized by an imbalance between different species of massless fermions. We use natural units ħ 1⁄4 c 1⁄4 kB 1⁄4 1 and the metric gμν 1⁄4 diagð1; −1; −1; −1Þ
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