Index formulas and charge deficiencies on the Landau levels

@article{Goffeng2010IndexFA,
  title={Index formulas and charge deficiencies on the Landau levels},
  author={Magnus Goffeng},
  journal={Journal of Mathematical Physics},
  year={2010},
  volume={51},
  pages={023509-023509}
}
  • Magnus Goffeng
  • Published 2 February 2010
  • Physics, Mathematics
  • Journal of Mathematical Physics
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. 
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References

SHOWING 1-10 OF 20 REFERENCES
Charge deficiency, charge transport and comparison of dimensions
We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the
Toeplitz operators on the Segal-Bargmann space
In this paper, we give a complete characterization of those functions on 2n-dimensional Euclidean space for which the Berezin-Toeplitz quantizations admit a symbol calculus modulo the compact
D-Branes, RR-Fields and Duality on Noncommutative Manifolds
We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane
On the Spectral Properties of the Perturbed Landau Hamiltonian
The Landau Hamiltonian governing the behavior of a quantum particle in dimension 2 in a constant magnetic field is perturbed by a compactly supported magnetic field and a similar electric field. We
Geometric K-Homology of Flat D-Branes
We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We
The Classification of Extensions of C *-algebras
where K = K(H) denotes the compact operators on a separable infinite-dimensional Hubert space H. The addition operation comes from associating to (1.1) its "Busby invariant" [4, Theorem 4.3] A —•
Harmonic analysis in phase space
This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related
A NOTE ON TOEPLITZ OPERATORS
We study Toeplitz operators on Bergman spaces using techniques from the analysis of Dirac-type operators on complete Riemannian manifolds, and prove an index theorem of Boutet de Monvel from this
On the index of Toeplitz operators of several complex variables
Toeplitz operators on strictly pseudo-convex boundaries of complex domains are defined; they behave like pseudo-differential operators. An extension of the Atiyah-Singer formula is proved for
Spectral shift function in strong magnetic fields
The three-dimensional Schrodinger operator H with constant magnetic field of strength b> 0 is considered under the assumption that the electric potential V ∈ L 1 (R 3 ) admits certain power-like
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