Beyond-Constant-Mass-Approximation Magnetic Catalysis in the Gauge Higgs-Yukawa Model

Beyond-constant-mass approximation solutions for magnetically catalyzed fermion and scalar masses are found in a gauge Higgs-Yukawa theory in the presence of a constant magnetic field. The obtained fermion masses are several orders of magnitude larger than those found in the absence of Yukawa interactions. The masses obtained within the beyond-constant-mass approximation exactly reduce to the results within the constant-mass approach when the condition $\nu \ln (\frac{1}{\hat{m}^{2}})\ll 1$ is satisfied. Possible applications to early universe physics and condensed matter are discussed.Comment: Revised numerical results. New figures. Several sections rewritte

Magnetism in Dense Quark Matter

We review the mechanisms via which an external magnetic field can affect the ground state of cold and dense quark matter. In the absence of a magnetic field, at asymptotically high densities, cold quark matter is in the Color-Flavor-Locked (CFL) phase of color superconductivity characterized by three scales: the superconducting gap, the gluon Meissner mass, and the baryonic chemical potential. When an applied magnetic field becomes comparable with each of these scales, new phases and/or condensates may emerge. They include the magnetic CFL (MCFL) phase that becomes relevant for fields of the order of the gap scale; the paramagnetic CFL, important when the field is of the order of the Meissner mass, and a spin-one condensate associated to the magnetic moment of the Cooper pairs, significant at fields of the order of the chemical potential. We discuss the equation of state (EoS) of MCFL matter for a large range of field values and consider possible applications of the magnetic effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Photon Propagation in Space-Time with a Compactified Spatial Dimension

The one-loop effects of vacuum polarization induced by untwisted fermions in QED in a nonsimply connected space-time with topology $S^{1}\times R^{3}$ are investigated. It is found that photon propagation in this system is anisotropic, appearing several massive photon modes and a superluminal transverse mode. For small compactification radius $a$, the superluminal velocity increases logarithmically with $a$. At low energies the photon masses lead to an effective confinement of the gauge fields into a (2+1)-dimensional manifold transverse to the compactified direction. The system shows a topologically induced directional superconductivity.Comment: 5 pages, to appear in PL

Hypermagnetic Field Effects in the Thermal Bath of Chiral Fermions

The dispersion relations for leptons in the symmetric phase of the electroweak model in the presence of a constant hypermagnetic field are investigated. The one-loop fermion self-energies are calculated in the lowest Landau level approximation and used to show that the hypermagnetic field forbids the generation of the ''effective mass'' found as a pole of the fermions' propagators at high temperature and zero fields. In the considered approximation leptons behave as massless particles propagating only along the direction of the external field. The reported results can be of interest for the cosmological implications of primordial hypermagnetic fields.Comment: 5 page

Neutrino Propagation in a Strongly Magnetized Medium

We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained for neutral and charged media in the strong-field limit ($M_{W}\gg \sqrt{B}\gg m_{e},T,\mu ,| \mathbf{p}|$) using the lowest Landau level approximation. The results found within the lowest Landau level approximation are numerically validated, summing in all Landau levels, for strong $B\gg T^{2}$ and weakly-strong $B \gtrsim T^{2}$ fields. The neutrino energy in leading order of the Fermi coupling constant is expressed as the sum of three terms: a kinetic-energy term, a term of interaction between the magnetic field and an induced neutrino magnetic moment, and a rest-energy term. The leading radiative correction to the kinetic-energy term depends linearly on the magnetic field strength and is independent of the chemical potential. The other two terms are only present in a charged medium. For strong and weakly-strong fields, it is found that the field-dependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered.Comment: 23 pages, 4 figures. Corrected misprints in reference

Boundary Effects in the Magnetic Catalysis of Chiral Symmetry Breaking

The catalysis of chiral symmetry breaking by an applied constant magnetic field and in the presence of boundaries along third axis is investigated in the four-dimensional Nambu-Jona-Lasinio model. It is shown that in case of periodic boundary conditions for fermions the magnetic field breaks the chiral symmetry, generating a dynamical mass even at the weakest attractive interaction between fermions. For antiperiodic boundary conditions the effect of the finite third dimension is to counteract the chiral symmetry breaking.Comment: 7 pages, revtex. Typos are corrected, references updated and new ones included, and added the calculation of the critical length in case of twisted fermion

Spontaneous symmetry breaking in gauge theories via Bose-Einstein condensation

We propose a mechanism naturally leading to the spontaneous symmetry breaking in a gauge theory. The Higgs field is assumed to have global and gauged internal symmetries. We associate a non zero chemical potential to one of the globally conserved charges commuting with all of the gauge transformations. This induces a negative mass squared for the Higgs field triggering the spontaneous symmetry breaking of the global and local symmetries. The mechanism is general and we test the idea for the electroweak theory in which the Higgs sector is extended to possess an extra global Abelian symmetry. To this symmetry we associate a non zero chemical potential. The Bose-Einstein condensation of the Higgs leads, at tree level, to modified dispersion relations for the Higgs field while the dispersion relations of the gauge bosons and fermions remain undisturbed. The latter are modified through higher order corrections. We have computed some corrections to the vacuum polarizations of the gauge bosons and fermions. To quantify the corrections to the gauge boson vacuum polarizations with respect to the Standard Model we considered the effects on the T parameter. We finally derive the one loop modified fermion dispersion relations.Comment: RevTeX 4, 13 pages. Added references and corrected typo

Phase Transition in Anyon Superconductivity at Finite Temperature

The magnetic response of the charged anyon fluid at temperatures larger than the fermion energy gap is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration, is found. The inhomogeneity is linked to the existence of an imaginary magnetic mass which increases with the temperature. The system stability in the new phase is proved by investigating the electromagnetic field rest-energy spectrum.Comment: 18 pages, revte

Magnetothermal Conductivity of Highly Oriented Pyrolytic Graphite in the Quantum Limit

We report on the magnetic field (0T$\le B \le 9$T) dependence of the longitudinal thermal conductivity $\kappa(T,B)$ of highly oriented pyrolytic graphite in the temperature range 5 K $\le T\le$ 20 K for fields parallel to the $c-$axis. We show that $\kappa(T,B)$ shows large oscillations in the high-field region (B > 2 T) where clear signs of the Quantum-Hall effect are observed in the Hall resistance. With the measured longitudinal electrical resistivity we show that the Wiedemann-Franz law is violated in the high-field regime.Comment: 4 Figures, to be published in Physical Review B (2003

Chiral fermion mass and dispersion relations at finite temperature in the presence of hypermagnetic fields

We study the modifications to the real part of the thermal self-energy for chiral fermions in the presence of a constant external hypermagnetic field. We compute the dispersion relation for fermions occupying a given Landau level to first order in g'^2, g^2 and g_phi^2 and to all orders in g'B, where g' and g are the U(1)_Y and SU(2)_L couplings of the standard model, respectively, g_phi is the fermion Yukawa coupling, and B is the hypermagnetic field strength. We show that in the limit where the temperature is large compared to sqrt{g'B}, left- and right-handed modes acquire finite and different B-dependent masses due to the chiral nature of their coupling with the external field. Given the current bounds on the strength of primordial magnetic fields, we argue that the above is the relevant scenario to study the effects of magnetic fields on the propagation of fermions prior and during the electroweak phase transition.Comment: 11 pages 4 figures, published versio