Kinetic derivation of generalized phase space Chern-Simons theory

TL;DR

This paper develops a kinetic theory in 2D phase space incorporating Berry curvature effects, deriving anomalous currents and formulating an effective Chern-Simons theory to describe these phenomena.

Contribution

It introduces a kinetic framework for phase-space Berry curvature and derives a corresponding 1+2D Chern-Simons effective theory for anomalous transport.

Findings

Derived anomalous currents from phase-space Poisson brackets

Constructed a 1+2D Chern-Simons effective theory

Discussed implications for anomalous transport phenomena

Abstract

We study anomalous transport phenomena induced by phase-space Berry curvature. For that purpose we construct a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive anomalous currents by calculating the complete form of the Poisson brackets of phase space coordinates. Then we construct the low-energy effective theory to reproduce the anomalous currents obtained from the kinetic theory. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.