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

TL;DR

This paper explores the connection between Chern-Simons theory and quantum fields in the lowest Landau level, deriving a Lagrangian and quantum formalism relevant for quantum Hall systems.

Contribution

It introduces a Chern-Simons type Lagrangian for electrons in the LLL and develops a quantum framework with complex gauge fields and transformations.

Findings

Derived a Chern-Simons type Lagrangian for LLL electrons

Presented formal expressions for Read's operator and Laughlin wave function

Established a quantum theory framework for matter fields in LLL

Abstract

By considering the area preserving geometric transformations in the configuration space of electrons moving in the lowest Landau level (LLL) we arrive at the Chern-Simons type Lagrangian. Imposing the LLL condition, we get a scheme with the complex gauge fields and transformations. Quantum theory for the matter field in LLL is considered and formal expressions for Read's operator and Laughlin wave function are presented in the second quantized form.