Index formulas and charge deficiencies on the Landau levels

Journal article, 2010

The notion of charge deficiency by Avron et al. [“Charge deficiency, charge transport and comparison of dimensions,” Commun. Math. Phys. 159, 399 (1994) ] is studied from the view of K-theory of operator algebras and is applied to the Landau levels in \R^{2n}. We calculate the charge deficiencies at the higher Landau levels in \R^{2n} by means of an Atiyah–Singer-type index theorem.