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

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

1994-03-16

arxiv.org/abs/hep-th/9403092v2

Int.J.Mod.Phys.A11:2065-2080,1996

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTeX, section added on unitarity of Chern-Simons theory and anomalies, general improvement

Scientific paper

10.1142/S0217751X96001048

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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