Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories

TL;DR

This paper explores how chiral dynamics in QED and QCD under strong magnetic fields relate to complex nonlocal noncommutative field theories, highlighting differences from NJL models and implications for condensed matter physics.

Contribution

It reveals the intricate nonlocal NCFT structures arising from gauge models in magnetic fields and distinguishes them from NJL models, emphasizing the role of interaction range.

Findings

Gauge models lead to complex nonlocal NCFTs with no simple field transformation.

Interactions are long-range in gauge theories, unlike short-range in NJL models.

Implications for quantum Hall effect in condensed matter systems are discussed.

Abstract

We study the connection of the chiral dynamics in QED and QCD in a strong magnetic field with noncommutative field theories (NCFT). It is shown that these dynamics determine complicated nonlocal NCFT. In particular, although the interaction vertices for electrically neutral composites in these gauge models can be represented in the space with noncommutative spatial coordinates, there is no field transformation that could put the vertices in the conventional form considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model in a magnetic field where such a field transformation can be found, with a cost of introducing an exponentially damping form factor in field propagators. The crucial distinction between these two types of models is in the characters of their interactions, being short-range in the NJL-like models and long-range in gauge theories. The relevance of the NCFT connected with the gauge models for the description of the quantum Hall effect in condensed matter systems with long-range interactions is briefly discussed.