Bosonization, mass generation, and the pseudo Chern-Simons action

TL;DR

This paper explores a generalized Chern-Simons action with a pseudo-differential operator, deriving it from bosonization in (2+1)D, and studies its effects on mass generation, particle interactions, and potential bound states in two-dimensional materials.

Contribution

It introduces the pseudo Chern-Simons (PCS) action derived from bosonization and analyzes its impact on gauge field mass and particle interactions in (2+1)D systems.

Findings

PCS induces mass in the gauge field without Higgs mechanism.

Bound states can form due to the interplay of Coulomb and attractive potentials.

PCS does not alter renormalization of Fermi velocity or band gap in Dirac materials.

Abstract

We discuss several aspects of a generalization of the Chern-Simons action containing the pseudo-differential operator$\sqrt{-\Box}$, which we shall call pseudo Chern-Simons (PCS). Firstly, we derive the PCS from the bosonization of free massive Dirac particles in (2+1)D in the limit when $m^2\ll p^2$, where $m$ is the fermion mass and $p$ is its momentum. In this regime, the whole bosonized action also has a modified Maxwell term, involving the same pseudo-differential operator. Furthermore, the large-mass $m^2\gg p^2$ regime is also considered. We also investigate the main effects of the PCS term into the Pseudo quantum electrodynamics (PQED), which describes the electromagnetic interactions between charged particles in (2+1)D. We show that the massless gauge field of PQED becomes massive in the presence of a PCS term, without the need of a Higgs mechanism. In the nonrelativistic limit, we show that the static potential has a repulsive term (given by the Coulomb potential) and an attractive part (given by a sum of special functions), whose competition generates bound states of particles with the same charge. Having in mind two-dimensional materials, we also conclude that the presence of a PCS term does not affect the renormalization either of the Fermi velocity and of the band gap in a Dirac-like material.