The quantum kinetic equation and dynamical mass generation in 2+1 Dimensions

TL;DR

This paper develops a relativistic quantum kinetic framework in 2+1 dimensions to analyze transport phenomena and dynamical mass generation, including effects of external fields and interactions.

Contribution

It introduces a systematic semi-classical expansion of Wigner function equations in 2+1D, revealing new transport currents and mechanisms for mass generation.

Findings

Derived parity-odd transport current induced by electromagnetic fields.

Identified a new transport current from the gradient of the mean-field condensate.

Explored dynamical mass generation in magnetic fields at equilibrium.

Abstract

In this work, we study the relativistic quantum kinetic equations in 2+1 dimensions from Wigner function formalism by carrying out a systematic semi-classical expansion up to $\hbar$ 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.