[Paper Review] QED Plasma at Finite Temperature up to Two Loops

Samina Masood|arXiv (Cornell University)|Aug 30, 2018

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper investigates quantum electrodynamics (QED) plasma at finite temperature up to two-loop order using real-time finite-temperature field theory. It demonstrates that higher-order corrections remain small compared to leading-order effects, confirming perturbative renormalizability of QED up to ~4 MeV, with key results showing quadratic temperature dependence of plasma parameters and consistent suppression of second-order contributions, validating Debye shielding and plasmon formation in early-universe conditions.

ABSTRACT

We study the vacuum polarization tensor of QED (quantum electrodynamics) at high temperatures up to the two loop levels and its effect on the electromagnetic properties of a medium. One loop corrections to QED coupling vanish at low temperatures (T$\leq 10^{10}K$), but they play an important role at high temperature ( T$\geq 10^{10}$ K) to study the behavior of QED medium at these temperatures. At low temperatures ( $T \leq m_e$)higher order loops give a tiny correction due to the coupling of radiation with matter and an overlap of hot photon loop with cold fermion loop contributes to this effect. These higher loop contributions does not affect the convergence of perturbative series, and renormalizability of QED is guaranteed at temperatures around neutrino decoupling. We use the renormalization scheme of QED at finite temperature in real-time formalism to study the dynamically generated mass of photon indicating the plasmon production in such a medium. Temperature dependence of this QED plasma parameters is discussed. We explicitly show that this behavior of a thermal medium exists upto temperatures of a few MeV only. We compare the first order and second order effects upto the 4MeV temperature and demonstrate that the higher order contributions are smaller than the lower order contributions proving the renormalizability of the theory. The lowest order contributions are sufficiently smaller than the original value as well.

Motivation & Objective

• To assess the renormalizability of QED at finite temperature using higher-loop corrections up to two loops.
• To examine the role of vacuum polarization and thermal corrections in modifying electromagnetic properties of a QED plasma.
• To determine the temperature range where plasmon effects and Debye shielding remain valid in hot QED media.
• To compare first- and second-order contributions in perturbation theory to validate the convergence and consistency of the effective field theory approach.

Proposed method

• Employing the real-time formalism of finite-temperature quantum field theory to compute thermal corrections to the vacuum polarization tensor.
• Using thermally corrected fermion propagators with finite-density distribution functions to incorporate medium effects.
• Calculating the vacuum polarization tensor up to two-loop order, including overlapping cold and hot propagator terms.
• Evaluating the dynamically generated photon mass and plasma screening effects via the Debye shielding length and plasmon frequency.
• Applying renormalization schemes to extract temperature-dependent corrections to the electric charge, electron mass, and wavefunction.
• Comparing first- and second-order contributions to photon frequency, momentum, and shielding parameters to test perturbative convergence.

Experimental results

Research questions

• RQ1 Does the perturbative series in QED remain convergent at finite temperature up to two-loop order, particularly in the range T ≤ 4 MeV?
• RQ2 How do higher-loop corrections affect the electromagnetic properties of a QED plasma, such as Debye shielding and plasmon dispersion?
• RQ3 To what extent do second-order contributions in α suppress or modify the leading-order behavior of plasma parameters like ωT² and κL²?
• RQ4 Is the renormalizability of QED preserved under finite-temperature corrections, especially when overlapping cold and hot loop terms are present?
• RQ5 What is the temperature dependence of the dynamically generated photon mass and how does it relate to the onset of plasma screening?

Key findings

• Second-order corrections to the transverse photon frequency ωT² and longitudinal wavenumber κL² are significantly smaller than first-order contributions, indicating perturbative stability.
• The Debye shielding length shows a clear dominance of first-order contributions, with second-order terms being negligible, confirming the validity of the screening approximation.
• All vacuum polarization components, including ωT² and κL², exhibit quadratic dependence on temperature (T²), consistent with thermal field theory expectations.
• The effective electric charge and coupling strength show temperature-dependent renormalization, but second-order corrections remain subdominant, supporting the renormalizability of QED at T ≤ 4 MeV.
• Plasmon effects and Debye shielding are confirmed to be physically relevant only up to temperatures of about 4 MeV, corresponding to the pre-nucleosynthesis era.
• The absence of significant pinch singularities and the consistent cancellation of divergences in the real-time formalism validate the calculational scheme up to two-loop order.