Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Systematics of High Temperature Perturbation Theory: The Two-Loop
  Electron Self-Energy in QED   In order to investigate the systematics of the loop expansion in high
temperature gauge theories beyond the leading order hard thermal loop (HTL)
approximation, we calculate the two-loop electron proper self-energy in high
temperature QED. The two-loop bubble diagram contains a linear infrared
divergence. Even if regulated with a non-zero photon mass M of order of the
Debye mass, this infrared sensitivity implies that the two-loop self-energy
contributes terms to the fermion dispersion relation that are comparable to or
even larger than the next-to-leading-order (NLO) contributions at one-loop.
Additional evidence for the necessity of a systematic restructuring of the loop
expansion comes from the explicit gauge parameter dependence of the fermion
damping rate at both one and two-loops. The leading terms in the high
temperature expansion of the two-loop self-energy for all topologies arise from
an explicit hard-soft factorization pattern, in which one of the loop integrals
is hard, nested inside a second loop integral which is soft. There are no
hard-hard contributions to the two-loop Sigma at leading order at high T.
Provided the same factorization pattern holds for arbitrary ell loops, the NLO
high temperature contributions to the electron self-energy come from ell-1 hard
loops factorized with one soft loop integral. This hard-soft pattern is both a
necessary condition for the resummation over ell to coincide with the one-loop
self-energy calculated with HTL dressed propagators and vertices, and to yield
the complete NLO correction to the self-energy at scales ~eT, which is both
infrared finite and gauge invariant. We employ spectral representations and the
Gaudin method for evaluating finite temperature Matsubara sums, which
facilitates the analysis of multi-loop diagrams at high T.

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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg