Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy 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.Comment: 15 pages, 5 figure

Effect of a Magnetic Field on the Electroweak Symmetry

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. Charged vector bosons play the most important role, leading only to a decrease of the symmetry breaking parameter, the symmetry restoration not being possible.Comment: Presented in the First International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2003), Olinda, Brazi

Constraint on the stem cell numbers and division rates posed by the risk of cancer

Compiled data for the stem cell numbers, Ns, and division rates, ms, is reanalized in order to show that we can distinguish two groups of human tissues. In the first one, there is a relatively high fraction of maintenance (stem and transit) cells in the tissue, but the division rates are low. The second group, on the other hand, is characterized by very high transit cell division rates, of around one division per day. These groups do not have an embrionary origin. We argue that their properties arise from a combination of the needs of tissue homeostasis (in particular turnover rate) and a bound on cancer risk, which is roughly a linear function of the product Ns ms. The bound on cancer risk leads to a threshold at ms = 8/year, where the fraction of stem cells falls down two orders of magnitude

The LHCb VELO Upgrade

LHCb is a forward spectrometer experiment dedicated to the study of new physics in the decays of beauty and charm hadrons produced in proton collisions at the Large Hadron Collider (LHC) at CERN. The VErtex LOcator (VELO) is the microstrip silicon detector surrounding the interaction point, providing tracking and vertexing measurements. The upgrade of the LHCb experiment, planned for 2018, will increase the luminosity up to $\rm 2\times10^{33}\ cm^{-2}s^{-1}$ and will perform the readout as a trigger-less system with an event rate of 40 MHz. Extremely non-uniform radiation doses will reach up to $\rm 5 \times 10^{15}$ 1 MeV$\rm n_{eq}/cm^2$ in the innermost regions of the VELO sensors, and the output data bandwidth will be increased by a factor of 40. An upgraded detector is under development based in a pixel sensor of the Timepix/Medipix family, with 55 x 55 $\rm \mu m^2$ pixels. In addition a microstrip solution with finer pitch, higher granularity and thinner than the current detector is being developed in parallel. The current status of the VELO upgrade program will be described together with recent testbeam results

Vacuum pressures and energy in a strong magnetic field

We study vacuum in a strong magnetic field. It shows a nonlinear response, as a ferromagnetic medium. Anisotropic pressures arise, and a negative pressure is exerted in the direction perpendicular to the field. The analogy of this effect with the Casimir effect is analyzed. The vacuum transverse pressure is found to be of the same order of the statistical pressure for $B\sim10^{15}G$ and $N\sim10^{33}electrons/cm^{3}$. Vacuum interaction with the field is studied also for $B\sim10^{16}G$ and larger, including the electron anomalous magnetic moment. We estimate quark contribution to vacuum behavior.Comment: Presented in the International Workshop on Strong Magnetic Fields and Neutron Stars, Havana, Cuba, April 200

The photon magnetic moment has not a perpendicular component and is fully paramagnetic

Our paper Phys. Rev. D \textbf{79}, 093002 (2009), in which it was shown the paramagnetic behavior of photons propagating in magnetized vacuum, is criticized in Phys. Rev. D \textbf{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

Is the photon paramagnetic?

A photon exhibits a tiny anomalous magnetic moment $\mu_{\gamma}$ due to its interaction with an external constant magnetic field in vacuum through the virtual electron-positron background. It is paramagnetic ($\mu_{\gamma}>0$) in the whole region of transparency, i.e. below the first threshold energy for pair creation and has a maximum near this threshold. The photon magnetic moment is different for eigenmodes polarized along and perpendicular to the magnetic field. Explicit expressions are given for $\mu_{\gamma}$ for the cases of photon energies smaller and closer to the first pair creation threshold. The region beyond the first threshold is briefly discussed

Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment

We start from the analytical expression of the eigenvalues $\kappa^{(i)}$ of the photon self-energy tensor in an external constant magnetic field $B$ calculated by Batalin Shabad in the Furry representation, and in the one-loop approximation. We expand in power series of the external field and in terms of the squared photon transverse momentum $z_2$ and (minus) transverse energy $z_1=k^2-z_2$, in terms of which are expressed $\kappa^{(i)}$. A general expression is given for the photon anomalous magnetic moment $\mu_{\gamma}>0$ in the region of transparency, below the first threshold for pair creation, and it is shown that it is positive, i.e. paramagnetic. The results of the numerical calculation for $\mu_{\gamma}>0$ are displayed in a region close to the threshold

Magnetic Fields in Quantum Degenerate Systems and in Vacuum

We consider self-magnetization of charged and neutral vector bosons bearing a magnetic moment in a gas and in vacuum. For charged vector bosons (W bosons) a divergence of the magnetization in both the medium and the electroweak vacuum occurs for the critical field B=B_{wc}=m_{w}^{2}/e. For B>B_{wc} the system is unstable. This behavior suggests the occurrence of a phase transition at B=B_{c}, where the field is self-consistently maintained. This mechanism actually prevents $B$ from reaching the critical value B_{c}. For virtual neutral vector bosons bearing an anomalous magnetic moment, the ground state has a similar behavior for B=B_{nbc}=m_{nb}^{2}/q . The magnetization in the medium is associated to a Bose-Einstein condensate and we conjecture a similar condensate occurs also in the case of vacuum. The model is applied to virtual electron-positron pairs bosonization in a magnetic field B \sim B_{pc}\lesssim 2m_{e}^{2}/e, where m_e is the electron mass. This would lead also to vacuum self-magnetization in QED, where in both cases the symmetry breaking is due to a condensate of quasi-massless particles

The paramagnetic photon. Absence of perpendicular component and decay in large fields

Previous results from the authors concerning the arising a tiny photon anomalous paramagnetic moment $\mu_{\gamma}$ due to its interaction with a magnetized virtual electron-positron background are complemented and discussed. It is argued that such magnetic moment it cannot be a linear function of the angular momentum and that there is no room for the existence of an hypothetical perpendicular component, as recently claimed in the literature. It is discussed that in the region beyond the first threshold, where photons may decay in electron-positron pairs, the photon magnetic moment cannot be defined independently of the magnetic moment of the created pairs. It is shown that for magnetic fields large enough, the vacuum becomes unstable and decays also in electron-positron pairs.Comment: Most of this paper is based on a talk presented at the International Workshop on Astronomy and Relativistic Astrophysics 2009 (IWARA09