Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-04
J.Phys.A41:355401,2008
Physics
High Energy Physics
High Energy Physics - Theory
15 pages. Accepted in Jour. Phys. A
Scientific paper
10.1088/1751-8113/41/35/355401
Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-space--time dimensions (QED$_3$), making use of the relativistic Kubo formula, we demonstrate that the filling factor accompanying the quantized electrical conductivity for massive Dirac fermions of a single species in two spatial dimensions is a half (in natural units) when time reversal and parity symmetries of the Lagrangian are explicitly broken by the fermion mass term. We then discuss the most general form of the QED$_3$ Lagrangian, both for irreducible and reducible representations of the Dirac matrices in the plane, with emphasis on the appearance of a Chern-Simons term. We also identify the value of the filling factor with a zero field quantum Hall effect (QHE).
Raya Alfredo
Reyes Edward D.
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