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Fixed typo. Now actually black revised version.
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ajsteinmetz committed Nov 8, 2023
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Expand Up @@ -414,7 +414,7 @@ \section{Gilbertian magnetization of electron-positron plasma}
\label{defmagetization}
{\cal M}\equiv\frac{T}{V}\frac{\partial}{\partial{\cal B}}\ln{{\cal Z}_{e^{+}e^{-}}} = \frac{T}{V}\left(\frac{\partial b_{0}}{\partial{\cal B}}\right)\frac{\partial}{\partial b_{0}}\ln{{\cal Z}_{e^{+}e^{-}}}\,,
\end{align}
Magnetization arising from other components in the cosmic gas (protons, neutrinos, etc.) could in principle also be included. Localized inhomogeneities of matter evolution are often non-trivial and generally be solved numerically using magneto-hydrodynamics (MHD)~\cite{melrose2008quantum,Vazza:2017qge,Vachaspati:2020blt,Stoneking:2020egj}. In the context of MHD, primordial magnetogenesis from fluid flows in the electron-positron epoch was considered in~\cite{Gopal:2004ut,Perrone:2021srr}. {\color{blue} We note in passing that the possible conservation of magnetic helicity~\cite{Boyarsky:2011uy}
Magnetization arising from other components in the cosmic gas (protons, neutrinos, etc.) could in principle also be included. Localized inhomogeneities of matter evolution are often non-trivial and generally be solved numerically using magneto-hydrodynamics (MHD)~\cite{melrose2008quantum,Vazza:2017qge,Vachaspati:2020blt,Stoneking:2020egj}. In the context of MHD, primordial magnetogenesis from fluid flows in the electron-positron epoch was considered in~\cite{Gopal:2004ut,Perrone:2021srr}. {\xblue We note in passing that the possible conservation of magnetic helicity~\cite{Boyarsky:2011uy}
relates to current induced magnetic fields. We do not expect this conservation law to hold for our Gilbertian spin based magnetization.
}
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