We study Faraday rotation in the quantum relativistic limit. Starting from the photon selfenergy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the fermion-antifermion gas is studied. The connection between Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect is also investigated for a massless relativistic (2D+1)-dimensional fermion system which is derived by using the compactification along the dimension parallel to the magnetic field. The Faraday angle shows a quantized behavior as Hall conductivity in two and three dimensions.

Our aim is to study the electron-positron vacuum pressures in presence of a strong magnetic field B. To that end, we obtain a general energy-momentum tensor, depending on external parameters, which in the zero temperature and zero density limit leads to vacuum expressions which are approximation-independent. Anisotropic pressures arise, and in the tree approximation of the magnetic field case, the pressure along B is positive, whereas perpendicular to B it is negative. Due to the common axial symmetry, the formal analogy with the Casimir effect is discussed, for which in addition to the usual negative pressure perpendicular to the plates, there is a positive pressure along the plates. The formal correspondence between the Casimir and black body energy-momentum tensors is analyzed. The fermion hot vacuum behavior in a magnetic field is also briefly discussed.

We discuss the effect of a strong magnetic field in the behavior of the symmetry of an electrically neutral electroweak plasma. We analyze the case of a strong field and low temperatures as compared with the W rest energy. If the magnetic field is large enough, it is self-consistently maintained. It is shown that the charged vector bosons play the most important role, leading only to a decrease of the symmetry breaking parameter, the symmetry restoration not being possible.

The rotation of the polarization vector for light propagating in an external constant magnetic field B in relativistic media is discussed in the two main cases: Faraday and Cotton–Mouton effects. Faraday rotation is circular and arises whenever the medium is not invariant under charge conjugation, whereas Cotton–Mouton rotation arises due to the breaking of the space symmetry in any transparent medium, and describes a sort of ellipse whose axes vary periodically in time from zero to two maximum values. The discussion starts from the expressions for the photon energy eigenvalues in vacuum as well as in a relativistic electron–positron gas, which remain valid in the low energy, low density limits. Values for the rotation frequencies are estimated in some specific cases. Our studies might be of interest both in experimental studies about light propagation in ultrahigh vacuum, as well as in astrophysics.

Under the action of field intensities around the Schwinger critical field, a dense electron gas behaves as unidimensional, exerting strong pressure along the applied field. We suggest a model for maintaining the magnetic field self-consistently, by assuming spin parallel pairing leading to a partial bosonization of the electron gas, which is described by a charged vector boson field, able to experience condensation, leading to a ferromagnetic behavior. Our aim is to suggest a possible quantum relativistic self-magnetized jet model. High frequency photons will be deviated also along paths parallel to the external field, leading to a model for a jet. Any addition of matter and/or energy to the electron system, would contribute to increase the kinetic energy along the magnetic field axis, an the jet may extend for long distances.

Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system C non-invariant under fermion-antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature the main features of quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to e 2 /h for the Hall conductivity . For typical values of graphene the plateaus of the Hall conductivity are also reproduced.2D massless QED Hall half-integer conductivity and graphene 2

The photon magnetic moment for radiation propagating in magnetized vacuum is defined as a pseudotensor quantity, proportional to the external electromagnetic field tensor. After expanding the eigenvalues of the polarization operator in powers of k 2 , we obtain approximate dispersion equations (cubic in k 2 ), and analytic solutions for the photon magnetic moment, valid for low momentum and/or large magnetic field. The paramagnetic photon experiences a redshift, with opposite sign to the gravitational one, which differs for parallel and perpendicular polarizations. It is due to the drain of photon transverse momentum and energy by the external field. By defining an effective transverse momentum, the constancy of the speed of light orthogonal to the field is guaranteed. We conclude that the propagation of the photon non-parallel to the magnetic direction behaves as if there is a quantum compression of the vacuum or a warp of space-time in an amount depending on its angle with regard to the field.

We discuss the behavior of a strongly magnetized electron gas whose dominant pressure is exerted along the applied field, and extends along it as a one dimensional system. We suggest a model for maintaining the magnetic field selfconsistently, and for it we conjecture a partial bosonization of the electron gas, described by a charged vector boson field which experiences condensation, leading to a ferromagnetic behavior. Our aim is to suggest a possible quantum relativistic self-magnetized jet model. High frequency photons will be deviated also along paths parallel to the external field. Any addition of energy to the electron system, would contribute mainly to increase the kinetic energy along the magnetic field axis, an the jet may grow in this way for long times.