The equation of state of a system of fermions in a uniform magnetic field is obtained in terms of the thermodynamic quantities of the theory by using functional methods. It is shown that the breaking of the O(3) rotational symmetry by the magnetic field results in a pressure anisotropy, which leads to the distinction between longitudinal-and transverse-to-the-field pressures. A criterion to find the threshold field at which the asymmetric regime becomes significant is discussed. This threshold magnetic field is shown to be the same as the one required for the pure field contribution to the energy and pressures to be of the same order as the matter contribution. A graphical representation of the field-dependent anisotropic equation of state of the fermion system is given. Estimates of the upper limit for the inner magnetic field in self-bound stars, as well as in gravitationally bound stars with inhomogeneous distributions of mass and magnetic fields, are also found.

We investigate the effects of an external magnetic field in the gap structure of a color superconductor with three massless quark flavors. Using an effective theory with four-fermion interactions, inspired by one-gluon exchange, we show that the long-range component B of the external magnetic field that penetrates the color-flavor locked (CFL) phase modifies its gap structure, producing a new phase of lower symmetry. A main outcome of our study is that the B field tends to strengthen the gaps formed by Q-charged and Q-neutral quarks that coupled among themselves through tree-level vertices. These gaps are enhanced by the field-dependent density of states of the Q-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.PACS numbers: 12.38. Aw, 24.85.+p After the suggestion that three-flavor quark matter may actually be the ground state of strong interactions [1], quark stars were postulated as possible astrophysical objects. It is also very likely that quark matter occupies the inner regions of neutron stars. Our present knowledge of QCD at high baryonic density indicates that this new state of matter might be in a color superconducting phase (for reviews, see [2]). On the other hand, it is well-known [3] that strong magnetic fields, as large as B ∼ 10 12 − 10 14 G, exist in the surface of neutron stars, while in magnetars they are in the range B ∼ 10 14 − 10 15 G, and perhaps as high as 10 16 G [4]. The physical upper limit to the total neutron star magnetic field, as arising from comparing the magnetic and gravitational energies, is of order B ∼ 10 18 G [3]. If quark stars are self-bound rather than gravitational-bound objects this upper limit could go higher. In this Letter we investigate the effect of a strong magnetic field in color superconductivity, with the aim of further studying its possible astrophysical implications.We will start by considering three massless quarks. In this case, it is well established that the ground state of high-dense QCD corresponds to the CFL (color-flavor locked) phase [5]. In this phase, quarks form spin-zero Cooper pairs in the color-antitriplet, flavor-antitriplet representation, thereby breaking the original SU (3) color × SU (3) L ×SU (3) R ×U (1) B symmetry to the diagonal subgroup SU (3) color+L+R . One can now ask how this scenario will change when a magnetic field is switched on. Would the external field affect the pairing phenomena? In a conventional electromagnetic superconductor, since Cooper pairs are electrically charged, the electromagnetic gauge invariance is spontaneously broken and the photon acquires a mass that can screen a weak magnetic field: this is the Meissner effect. In spin-zero color superconductivity, although the color condensate has nonzero electric charge, there is a linear combination of the photon and a gluon that remains massless [5]. The unbroken U (1) group is generated, in flavor-color space, by Q = Q × 1 − 1 × Q, where Q is the electromagnetic charge generator [6]. Thus a spi...

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 (MW ≫ √ B ≫ me, T, µ, |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 ≫ T 2 and weakly-strong B 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 restenergy 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 fielddependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered. PACS numbers: 13.15.+g, 14.60.Pq, 95.30.Cq, 98.80.Cq * Presently on leave at:

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state (EoS) of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent "bag constant" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs. bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

The best natural candidates for the realization of color superconductivity are quark stars -not yet confirmed by observation-and the extremely dense cores of compact stars, many of which have very large magnetic fields. To reliably predict astrophysical signatures of color superconductivity, a better understanding of the role of the star's magnetic field in the color superconducting phase that realizes in the core is required. This paper is an initial step in that direction. The field scales at which the different magnetic phases of a color superconductor with three quark flavors can be realized are investigated. Coming from weak to strong fields, the system undergoes first a symmetry transmutation from a Color-Flavor-Locked (CFL) phase to a Magnetic-CFL (MCFL) phase, and then a phase transition from the MCFL phase to the Paramagnetic-CFL (PCFL) phase.The low-energy effective theory for the excitations of the diquark condensate in the presence of a magnetic field is derived using a covariant representation that takes into account all the Lorentz structures contributing at low energy. The field-induced masses of the charged mesons and the threshold field at which the CFL → MCFL symmetry transmutation occurs are obtained in the framework of this low-energy effective theory. The relevance of the different magnetic phases for the physics of compact stars is discussed.