Michael Strickland, Veronica Dexheimer, Debora P. Menezes
In this paper we calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We compute the resulting transverse and longitudinal pressures using standard kinetic theory definitions. We present explicit formulae appropriate for zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. In the case of vanishing anomalous magnetic moment we demonstrate that the resulting expressions satisfy the canonical relations, Omega = - P_parallel and P_perp = P_parallel - M B with M = - d Omega/d B being the magnetization of the system. However, we find that the latter relation does not hold when the particles have a non-vanishing anomalous magnetic moment. In this case one must use the kinetic theory formulation for the transverse pressure.
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http://arxiv.org/abs/1209.3276
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