Abstract
We study the Quantum Faraday rotation starting from the photon self-energy in the presence of a constant magnetic field. The Faraday angle is calculated in the non-degenerate regime and for weak field limit. Two physical scenarios, possibly characterized by these conditions, are the recombination epoch and the jets originated in pulsars. We discuss the resonant behavior that the Faraday angle exhibits in these scenarios and investigate the possibility of detecting cosmic magnetic fields through this resonant mechanism.
Highlights
Faraday effect 1 is the well known phenomenon where plane polarized light penetrating in a magnetized transparent charged medium and moving parallel to the magnetic field B rotates its plane of polarization as a consequence of birefringence: the incoming wave splits in two opposite circularly polarized modes moving with different speeds, and the polarization vector rotates.Faraday Rotation (FR) is a particular case of the general problem of photon propagation in a charged medium 2
We study the Quantum Faraday rotation starting from the photon self-energy in the presence of a constant magnetic field
For 70GHz we obtain a value of the magnetic field 7.1 × 10−6G which is of the same order than the bound imposed by Faraday rotation from Plank through the semi-classical expression, far from the cyclotron frequency
Summary
Faraday effect 1 is the well known phenomenon where plane polarized light penetrating in a magnetized transparent charged medium and moving parallel to the magnetic field B rotates its plane of polarization as a consequence of birefringence: the incoming wave splits in two opposite circularly polarized modes moving with different speeds (and frequencies), and the polarization vector rotates. 3,4 we studied the relation between Faraday angle and Hall conductivity, showing their quantized feature It was done on the basis of the detailed study of general properties of the photon self-energy and the dispersion equations for photons propagating in the medium, parallel and perpendicular to the magnetic field, considering that the photon self-energy satisfies properties of gauge, Lorentz and CPT invariance 2. The first one is a cosmological scenario, where primordial magnetic fields (PMF), possibly present at the recombination epoch, can be estimated in the polarization of the Cosmic Microwave Background (CMB). In this case, we will be able to compare our results with the ones obtained by Planck 5. In Sec.[4] we state the concluding remarks
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