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

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.

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

Cited by in corpus (1)

• Chern-Simons Theory and Quantum Fields in the Lowest Landau Level