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Stability of large scale chromomagnetic fields in the early universe

Per Elmfors·David Persson
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Abstract

It is well known that Yang-Mills theory in vacuum has a perturbative instability to spontaneously form a large scale magnetic field (the Savvidy mechanism) and that a constant field is unstable so that a possible ground state has to be inhomogenous over the non-perturbative scale Lambda (the Copenhagen vacuum). We argue that this spontaneous instability does not occur at high temperature when the induced field strength gB ~ Lambda^2 is much weaker than the magnetic mass squared (g^2T)^2. At high temperature oscillations of gauge fields acquire a thermal mass M ~ gT and we show that this mass stabilizes a magnetic field which is constant over length scales shorter than the magnetic screening length (g^2T)^{-1}. We therefore conclude that there is no indication for any spontaneous generation of weak non-abelian magnetic fields in the early universe.

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Per Elmfors, David Persson. 1998-09-20. Stability of large scale chromomagnetic fields in the early universe. https://doi.org/10.1016/s0550-3213(98)00627-0

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