Dear all,

We remind you about tomorrow's seminar.

⟶ *Speaker:* Umberto Morellini (Université Paris Dauphine)

⟶ *Date:* Thursday 27th June, 11:00

⟶ *Where: *Aula Seminari (Pisa) and online on Google Meet: https://seminarimap.wixsite.com/seminarimap/2023-2024-1/umberto-morellini https://seminarimap.wixsite.com/seminarimap/2023-2024-1/octave-mischler

⟶ *Title:* The free energy of Dirac’s vacuum in purely magnetic fields

⟶ *Abstract:* *The Dirac vacuum is a non-linear polarisable medium rather than an empty space. This **non-linear behaviour starts to be significant for extremely large electromagnetic fields such as the **magnetic field on the surface of certain neutron stars. Even though the null temperature case was **deeply studied in the past decades, the problem at non-zero temperature needs to be better under**stood. **In this talk, we will present the first rigorous derivation of the one-loop effective magnetic La* *grangian **at positive temperature, a non-linear functional describing the free energy of quantum **vacuum in a classical magnetic field. After introducing our model, we will properly define the free **energy functional using the Pauli-Villars regularisation technique in order to remove the worst **ul**traviolet divergences, which represent a well known issue of the theory. The study of the properties **of this functional will be addressed before focusing on the limit of slowly varying classical magnetic **fields. In this regime, one can prove the convergence of this functional to the Euler-Heisenberg **formula with thermal corrections, recovering the effective Lagrangian first derived by Dittrich in **1979. The talk is based on the work available at arXiv:2404.12733.*

We remind you that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

For more information, check our website: https://seminarimap.wixsite.com/seminarimap

See you soon,

The organizers: Jeremy Mirmina Filippo Paiano Mario Rastrelli Leonardo Roveri

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