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Keywords:

  • Fractional quantum Hall liquids;
  • edge states;
  • field theories with boundary.

Abstract

The method of separability, introduced by Symanzik, is applied in order to describe the effect of a boundary for a fractional quantum Hall liquid in the Laughlin series. An Abelian Chern-Simons theory with plane boundary is considered and the Green functions both in the bulk and on the edge are constructed, following a rigorous, perturbative, quantum field theory treatment. We show that the conserved boundary currents find an explicit interpretation in terms of the continuity equation with the electron density satisfying the Tomonaga-Luttinger commutation relation.