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Unitarity of The Realization of Conformal Symmetry in The Quantum Hall Effect

Jose Gaite
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Abstract

We study the realization of conformal symmetry in the QHE as part of the $W_\infty$ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts to taking proper care of the quantum measure. The consequences of unitarity for the Chern-Simons theory of the QHE are also studied, showing the connection of non-unitarity with anomalies. Finally, we discuss the geometrical paradox of realizing conformal transformations as area preserving diffeomorphisms.

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Jose Gaite. 1995-04-07. Unitarity of The Realization of Conformal Symmetry in The Quantum Hall Effect. https://doi.org/10.1142/s0217751x96001048

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