We investigate the effects of the anomalous magnetic moment (AMM) in the equation of state (EoS) of a system of charged fermions at finite density in the presence of a magnetic field. In the region of strong magnetic fields (eB > m 2 ) the AMM is found from the one-loop fermion self-energy. In contrast to the weak-field AMM found by Schwinger, in the strong magnetic field region the AMM depends on the Landau level and decreases with it. The effects of the AMM in the EoS of a dense medium are investigated at strong and weak fields using the appropriate AMM expression for each case. In contrast with what has been reported in other works, we find that the AMM of charged fermions makes no significant contribution to the EoS at any field value.

We study the one-loop gluon polarization tensor at zero and finite temperature in the presence of a magnetic field, to extract the thermomagnetic evolution of the strong coupling α s . We analyze four distinct regimes, to wit, the small and large field cases, both at zero and at high temperature. From a renormalization group analysis, we show that at zero temperature, either for small or large magnetic fields, and for a fixed transferred momentum Q 2 , α s grows with the field strength with respect to its vacuum value. However, at high temperature and also for a fixed value of Q 2 , we find two different cases. When the magnetic field is even larger than the squared temperature, α s also grows with the field strength. On the contrary, when the squared temperature is larger than the magnetic field, a turnover behavior occurs, and α s decreases with the field strength. This thermomagnetic behavior of α s can help explain the inverse magnetic catalysis phenomenon found by lattice QCD calculations. DOI: 10.1103/PhysRevD.98.031501 Strongly interacting matter exhibits unusual properties when subject to magnetic fields. It has been shown by lattice QCD (LQCD) that both the pseudocritical temperature for the chiral or deconfinement phase transition and the quark condensate for temperatures above the pseudocritical temperature decrease with the field strength. This phenomenon has been named "inverse magnetic catalysis" (IMC). The name implies the unexpected and opposite behavior to the zero temperature case, whereby the quark condensate increases monotonically with the field strength [1]. Within a framework born out from LQCD simulations, this phenomenon can be attributed to the competition between the so-called sea and valence contributions to the quark condensate, around the transition temperature. Indeed, when the condensate is computed from the QCD partition function, there are two distinct magnetic field-dependent factors: the determinant of the Dirac operator appearing when integrating out the fermion fields and the trace of the Dirac operator. The sea and valence contributions refer to the case where the magnetic field effect is only considered either in the determinant or in the trace of the Dirac operator, respectively. Although this separation seems artificial, it could apparently be placed on firmer grounds by resorting to LQCD techniques [2].Another scenario to explain the origin of IMC is that the strong coupling receives thermomagnetic corrections which make it increase or decrease depending on the competition between thermal and magnetic effects. The growth or decrease of the quark condensate would in turn be linked to the corresponding behavior of the coupling at zero or at high temperature, respectively. This scenario has been studied within effective QCD models [3][4][5][6][7][8][9], from the Schwinger-Dyson approach [10], and from the thermomagnetic behavior of the quark-gluon vertex in QCD [11,12]. In the latter, it has been shown that the growth or decrease of the effective QCD coupling, at finite...

The effect of magnetic fields in the Equations of State (EoS) of compact objects is the splitting of the pressure in two components, one parallel and the other perpendicular to the magnetic field. This anisotropy suggests the necessity of using structure equations considering the axial symmetry of the magnetized system. In this work, we consider an axially symmetric metric in spherical coordinates, the γ-metric, and construct a system of equations to describe the structure of spheroidal compact objects. In addition, we connect the geometrical parameter γ linked to the spheroid's radii, with the source of the anisotropy. So, the model relates the shape of the compact object to the physics that determines the properties of the composing matter. To illustrate how our structure equations work, we obtain the mass-radii solutions for magnetized White Dwarfs. Our results show that the main effect of the magnetic field anisotropy in White Dwarfs structure is to cause a deformation of these objects. Since this effect is only relevant at low densities, it does not affect the maximum values of magnetized White Dwarf's masses, which remain under Chandrasekhar limit. arXiv:1807.09943v3 [astro-ph.HE]