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Symanzik's method applied to fractional quantum Hall edge states
Article first published online: 15 AUG 2008
Copyright © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 17, Issue 11, pages 885–896, November 2008
How to Cite
Blasi, A., Ferraro, D., Maggiore, N., Magnoli, N. and Sassetti, M. (2008), Symanzik's method applied to fractional quantum Hall edge states. Ann. Phys., 17: 885–896. doi: 10.1002/andp.200810323
- Issue published online: 21 OCT 2008
- Article first published online: 15 AUG 2008
- Manuscript Accepted: 7 JUL 2008
- Manuscript Received: 23 JUN 2008
- Fractional quantum Hall liquids;
- edge states;
- field theories with boundary.
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.