LAUSR

In this work, we study the relativistic quantum kinetic equations in $2+1$ dimensions from Wigner function formalism by carrying out a systematic semiclassical expansion up to $\ensuremath{\hbar}$ order. The derived equations allow us to explore interesting transport phenomena in $2+1$ dimensions. Within this framework, the parity-odd transport current induced by the external electromagnetic field is self-consistently derived. We also examine the dynamical mass generation by implementing four-fermion interaction with mean-field approximation. In this case, a new kind of transport current is found to be induced by the gradient of the mean-field condensate. Finally, we also utilize this framework to study the dynamical mass generation in an external magnetic field for the ($2+1$)-dimensional system under equilibrium.