High energy neutrino oscillation at the presence of the Lorentz Invariance Violation

Due to quantum gravity fluctuations at the Planck scale, the space-time manifold is no longer continuous, but discretized. As a result the Lorentz symmetry is broken at very high energies. In this article, we study the neutrino oscillation pattern due to the Lorentz Invariance Violation (LIV), and compare it with the normal neutrino oscillation pattern due to neutrino masses. We find that at very high energies, neutrino oscillation pattern is very different from the normal one. This could provide an possibility to study the Lorentz Invariance Violation by measuring the oscillation pattern of very high energy neutrinos from a cosmological distance.Comment: 11 pages, 6 figure

Generation of circular polarization of CMB due to the Euler-Heisenberg Lagrangian

It is known that the dominated contribution of primordial anisotropies of Cosmic Microwave Background (CMB) are linearly polarized via Compton scattering. However circular polarization of this anisotropy are not observed up to now, but it has not been excluded in observational evidences. Here we show that Euler-Heisenberg Effective Lagrangian can generate circular polarization in CMB. This generation is calculated by using Quantum Boltzman Equation for time evolution of Stokes parameter. Also we estimate Faraday conversion phase in order of 10−13 due to this Lagrangian which gives lower bound on circular polarization of CMB.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

Euler-Heisenberg Lagrangian and photon circular polarization

Considering the effective Euler-Heisenberg Lagrangian, i.e., nonlinear photon-photon interactions, we study the circular polarization of electromagnetic radiation based on the time evolution of Stokes parameters. To the leading order, we solve the quantum Boltzmann equation for the density matrix describing an ensemble of photons in the space of energy-momentum and polarization states, and calculate the intensity of circular polarizations. Applying these results to a linear polarized thermal radiation, we calculate the circular-polarization intensity, and discuss its possible relevance to the circular polarization intensity of the cosmic microwave background radiation