The photon magnetic moment has not a perpendicular component and is fully paramagnetic
Abstract
Our paper Phys. Rev. D 79, 093002 (2009), in which it was shown the paramagnetic behavior of photons propagating in magnetized vacuum, is criticized in Phys. Rev. D 81, 105019, (2010) and even claimed that the photon has a diamagnetic component. Here it is shown that such criticism is inadequate and that the alleged "perpendicular component" is due to a mistake in differentiating a vanishing term with regard to the magnetic field B, or either by mistaking the derivative of a scalar product as that of a dyadic product. A discussion on the physical side of the problem is also made.
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