The spectrum consistency of fractional quantum Hall effect model

TL;DR

This paper analyzes the spectrum consistency of a fractional quantum Hall effect model, identifying issues with unitarity and proposing a reformulation that ensures a physically consistent quantum theory.

Contribution

It demonstrates how to properly formulate the gauge fields in the model to eliminate negative norm states and achieve spectrum consistency.

Findings

Original action violates unitarity due to negative norm states.

Reformulated action with fundamental gauge fields is spectrum consistent.

Model is now suitable for further quantization.

Abstract

The spectrum consistency of the three fermion family $U(1)\times U(1)$ quantum electrodynamics in three space-time dimensions [Phys. Rev. Lett. 124 (2020) 131601] is analyzed. It has been verified that the originally proposed action violates the unitarity consistency condition in the gauge field sector by exhibiting negative norm states in the spectrum. However, the cure came through the fundamental gauge fields properly settled, consequently, the action rewritten in terms of those fundamental fields shows to be free from any spurious degrees of freedom, and the model now becomes safe for further quantization.