Quantum hall effect on grassmann manifolds

Ballı, Fatih
In this work we formulate Quantum Hall E ect(QHE) on Grassmann manifolds Gr2(CN). We, rst give a self-contained reviews of integer QHE on R2, S2 CP1 and CP2 which are oriented towards our purposes. Then, we set up the Landau problem on Gr2(CN) and discuss and formulate the wave functions, energy levels, degeneracy, incompressibility and spatial density properties. Group theoretical techniques are used to explore these properties for both abelian and non-abelian backgrounds and the wave functions are expressed in terms of suitably restricted subset of Wigner-D functions. For the simplest case of QHE on Gr2(C4) with pure U(1) gauge elds, we introduce Plücker coordinates and express the wave functions and the gauge elds in these coordinates. We calculate the two-point correlation function and deduce the incompressibility of Quantum Hall liquid on Gr2(C4). We indicate how these formulation in local coordinates may be generalized to all Gr2(CN).


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In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
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Citation Formats
F. Ballı, “Quantum hall effect on grassmann manifolds,” M.S. - Master of Science, Middle East Technical University, 2014.