Abstract
Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the ν=1 integer quantum Hall effect (IQHE) state on the \(\nu=\frac{1}{2p+1}\) fractional quantum Hall effect (FQHE) states. Using the hydrodynamical description of the quantum Hall fluid, it is shown that these transformations are generated by vector fields satisfying the Gauss law in the interacting non-commutative Chern–Simons gauge theory, and the corresponding field-theory Lagrangian is reconstructed. It is demonstrated that the geometric transformations induce quantum-mechanical non-unitary similarity transformations, establishing the interplay between integral and fractional QHEs.
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