# Improved ring potential of QED at finite temperature in the limit of weak and strong magnetic fields

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## Recording Details

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PIRSA Number:
08060155

## Abstract

Using the general structure of the vacuum polarization tensor at non-zero temperature T and finite magnetic field B, the ring contribution to QED effective potential is determined beyond the static (zero momentum) limit. In the limit of weak magnetic field and at high temperature, the improved ring potential consists of a term proportional to T4®5=2, in ad-dition to the well-known T4®3=2 term. In the limit of strong magnetic field, where QED dynamics is dominated by the lowest Landau level (LLL), the ring potential consists of a novel term proportional to 2¼eB m2 ln ¡2®¼ eB m2 ¢. Using the full effective potential including both the one-loop effective and the improved ring potentials, QED gap equation is determined and the dynamical fermion mass generation is studied in the regime of LLL dominance at non-zero temperature. It is shown that at high temperature limit, where the thermal fluctuations dominate the magnetic catalysis of dynamical chiral symmetry breaking in LLL, a chiral symmetry restoration occurs at certain critical temperature Tc. But, comparing to Tc in the static limit, the critical temperature arising from the improved ring potential is lower.The improved ring contribution is also relevant in studying the electroweak phase transition in the presence of external (strong) magnetic fields [1]. PACS numbers: 11.10.Wx, 11.15.Ex, 12.38.Gc