Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

TL;DR

This paper explores how strong magnetic fields in QED lead to noncommutative gauge symmetry and nondecoupling phenomena, affecting gauge invariance and boundary dynamics in the infrared regime.

Contribution

It demonstrates the nondecoupling of higher Landau levels in QED under strong magnetic fields and links the dynamics to noncommutative QED and boundary effects.

Findings

LLL dominance transforms U(1) gauge symmetry into noncommutative U(1)

Higher Landau levels do not decouple in the infrared, causing symmetry restoration

Boundary dynamics at spatial infinity are crucial in the phenomena

Abstract

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative $U(1)_{nc}$ gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.