Progress on Chiral Symmetry Breaking in a Strong Magnetic Field

The problem of chiral symmetry breaking in QED in a strong magnetic field is briefly reviewed. Recent progress on issues regarding the gauge fixing independence of the dynamically generated fermion mass is discussed. Gauge theories play an important role in our understanding of a wide variety of phenomena in many areas of physics, ranging from the descriptions of fundamental interactions in elementary particle physics to the study of high temperature superconductivity in condensed matter physics. While the usual perturbative approach based on the loop expansion is sufficient in most circumstances, there are many interesting phenomena that can be understood only through a nonperturbative analysis. Examples include strong coupling gauge theories (such as QCD and hadron physics) as well as gauge fields under the influence of extreme conditions (such as high temperature and/or high density, strongly out-of-equilibrium instabilities, and strong external fields). Several methods have been developed to study nonperturbative phenomena in gauge theories. Lattice approach based on discretized descriptions is well suited for studying strong coupling gauge theories, especially the properties in vacuum or at finite temperature. New approach based on the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence offers the possibility to study strong coupling gauge theories by performing perturbative calculations in their gravity duals. Yet, field theoretical continuum approaches such as the Schwinger–Dyson (SD) equations and the effective action provide a natural framework for studies of nonperturbative phenomena in gauge theories. In particular, continuum descriptions are capable of describing dynamical real-time quantities in gauge fields under