We calculate the condensate and the vacuum current density induced by external static magnetic fields in (2+1) dimensions. At the perturbative level, we consider an exponentially decaying magnetic field along one Cartesian coordinate. Nonperturbatively, we obtain the fermion propagator in the presence of a uniform magnetic field by solving the Schwinger-Dyson equation in the rainbow-ladder approximation. In the large flux limit, we observe that both these quantities, either perturbative (inhomogeneous) and nonperturbative (homogeneous), are proportional to the external field, in agreement with early expectations.

A nonperturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics. In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED but also in its 3-dimensional counterpart. Employing this convenient form of the vertex ansatz into the Schwinger-Dyson equation for the fermion propagator, we observe that it renders the critical coupling in 4-dimensional quenched QED markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and dynamical chiral symmetry breaking in 3-dimensional quenched QED. DOI: http://dx.doi.org/10.1103/PhysRevD.84.036013 © 2011 American Physical Society

We evaluate the impact of an external magnetic field on the chiral symmetry and confinement–deconfinement transition temperatures by using a vector–vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature T and magnetic field strength eB ( e represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral ( T c χ ) and deconfinement ( T _c ^c ) transitions from their inflection points, respectively. By construction, T c χ = T c c in the chiral limit. Within a mean-field approximation, we observe the magnetic catalysis phenomenon, characterized by a rising behavior of T c χ and T _c ^c with growing eB . By considering a lattice-inspired running coupling which monotonically decreases with eB , inverse magnetic catalysis takes place in our model. We explore the role of the magnetic field in the traits of the confinement–deconfinement transition described by the model. Our findings are also in agreement with predictions derived from effective models of strong interactions.