Fadeev Jackiw Analysis of Constraints on Noncomutative Hall Effect

TL;DR

This paper applies Fadeev-Jackiw analysis to a Chern-Simons gauge theory for the Hall effect, extending it to noncommutative space to reveal new constraint relations and modifications to conductivity.

Contribution

It introduces a noncommutative extension of the Chern-Simons gauge theory for the Hall effect using Fadeev-Jackiw analysis, highlighting new constraint relations and conductivity adjustments.

Findings

Noncommutative constraints alter the gauge theory structure.

An adjustment factor on conductivity emerges from noncommutative effects.

The approach unifies classical and integer Hall effect descriptions.

Abstract

Constrained systems are fundamental to understanding of several physical realities. Even so the Hall effect is one of more revisited issue we can still find new approaches to obtain old and new important relations. In this paper a semi classical formulation is considered where an Chern-Simons gauge invariant theory is constructed for a Schroedinger field. The main idea is to describe both classical and integer Hall effect. We build up the constraints this model by means of the Fadeev-Jackiw quantization algorithm. In a second step we consider a noncommutative extension to the action. In this extended approach noncommutative constraints relations are obtained and guide us to an interesting adjustment factor on the conductivity expression.