Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-04-08
Annals Phys. 230 (1994) 131-144
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, Plain tex, CCNY-HEP-93/1
Scientific paper
10.1006/aphy.1994.1020
Starting from a system of planar electrons in a strong magnetic field normal to the plane, interacting with perturbing electromagnetic fields, an effective Lagrangian for the fermions in the lowest Landau level (L.L.L.) has been derived. By choosing a suitable background electrostatic potential, an incompressible droplet of these electrons is constructed. The gauge invariant effective Lagrangian for the electrons in the L.L.L. is shown to split naturally into a $1+1$ dimensional Lagrangian for the electrons on the surface of the droplet and into a $2+1$ dimensional gauge-field Lagrangian representing the contribution of the interior of the droplet. Upon bosonization, the former represents the surface vibrations of the droplet. Individually neither of these two actions is gauge invariant, but it is shown that the gauge dependence from the two pieces cancels out. This demonstrates that the edge degrees of freedom are essential for maintaining gauge invariance.
Ray Rashmi
Sakita Bunji
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