Symanzik's Method Applied To The Fractional Quantum Hall Edge States

TL;DR

This paper applies Symanzik's method to abelian Chern-Simons theory with boundaries, systematically deriving edge state results in the Laughlin series and connecting boundary currents to physical conservation laws and Luttinger liquids.

Contribution

It introduces a systematic approach using Symanzik's method to derive edge states in fractional quantum Hall systems, clarifying boundary current interpretations.

Findings

Edge states derived systematically from Symanzik's approach.

Boundary currents interpreted via continuity equation.

Recovery of Tomonaga-Luttinger relations for electronic density.

Abstract

In this paper we consider an abelian Chern-Simons theory with plane boundary and we show, following Symankiz's quite general approach, how the known results for edge states in the Laughlin series can be derived in a systematic way by the separability condition. Moreover we show that the conserved boundary currents find a natural and explicit interpretation in terms of the continuity equation and the Tomonaga-Luttinger commutation relation for electronic density is recovered.