$\bar{\psi} \psi$-condensate in constant magnetic fields

Abstract

We solve Dirac equation in the presence of a constant magnetic field in (3+1)- and (2+1)-dimensions. Quantizing the fermion field, we calculate $\bar{\psi} \psi$-condensate from first principles for parity conserving and violating Lagrangians for arbitrary field strength. We make comparison with the results already known in the literature for some particular cases and point out the relevance of our work for possible physical applications.