Plasmons, Magnetoplasmons and the \nu = 1/2 Quantum Hall Effect

Abstract

We address the problem of separating the short-distance, high-energy physics of cyclotron motion from the long- distance, low-energy physics within the Lowest Landau Level in field theoretic treatments of the Fractional Quantum Hall Effect. We illustrate our method for the case $\nu =1/2$. By a sequence of field transformations we go from electrons to fermions that carry flux tubes of thickness $l_o$ (cyclotron radius) and couple to harmonic oscillators corresponding to magnetoplasmons. The fermions keep track of the low energy physics while the oscillators describe the Landau level, cyclotron currents etc. From this starting point we are able to get Jain and Rezayi-Read wavefunctions, and many subsequent modifications of the RPA analysis of Halperin, Lee and Read.