Neutrino dispersion in external magnetic fields

We calculate the neutrino self-energy operator Sigma (p) in the presence of a magnetic field B. In particular, we consider the weak-field limit e B << m_\ell^2, where m_\ell is the charged-lepton mass corresponding to the neutrino flavor \nu_\ell, and we consider a "moderate field" m_\ell^2 << e B << m_W^2. Our results differ substantially from the previous literature. For a moderate field, we show that it is crucial to include the contributions from all Landau levels of the intermediate charged lepton, not just the ground-state. For the conditions of the early universe where the background medium consists of a charge-symmetric plasma, the pure B-field contribution to the neutrino dispersion relation is proportional to (e B)^2 and thus comparable to the contribution of the magnetized plasma.Comment: 9 pages, 1 figure, revtex. Version to appear in Phys. Rev. D (presentation improved, reference list revised, numerical error in Eq.(41) corrected, conclusions unchanged

Propagation of axions in a strongly magnetized medium

The polarization operator of an axion in a degenerate gas of electrons occupying the ground-state Landau level in a superstrong magnetic field $H\gg H_0=m_e^2c^3/e\hbar =4.41\cdot 10^{13}$ G is investigated in a model with a tree-level axion-electron coupling. It is shown that a dynamic axion mass, which can fall within the allowed range of values $(10^{-5} eV \lesssim m_a\lesssim 10^{-2} eV)$, is generated under the conditions of strongly magnetized neutron stars. As a result, the dispersion relation for axions is appreciably different from that in a vacuum.Comment: RevTex, no figures, 13 pages, Revised version of the paper published in J. Exp. Theor. Phys. {\bf 88}, 1 (1999

Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum