Relativistic field theories in a magnetic background as noncommutative field theories

TL;DR

This paper explores how relativistic field theories in strong magnetic fields relate to noncommutative field theories, revealing unique properties like absence of UV/IR mixing and dimensional reduction, with implications for confinement and finiteness.

Contribution

It demonstrates that the noncommutative field theories derived from relativistic models in magnetic backgrounds differ from traditional NCFT, especially regarding UV/IR mixing and dimensional behavior.

Findings

NCFT are different from conventional ones, lacking UV/IR mixing.

In certain magnetic configurations, NCFT are finite for even dimensions.

The dynamics become quasi-(1+1)-dimensional for odd dimensions.

Abstract

We study the connection of the dynamics in relativistic field theories in a strong magnetic field with the dynamics of noncommutative field theories (NCFT). As an example, the Nambu-Jona-Lasinio models in spatial dimensions $d \geq 2$ are considered. We show that this connection is rather sophisticated. In fact, the corresponding NCFT are different from the conventional ones considered in the literature. In particular, the UV/IR mixing is absent in these theories. The reason of that is an inner structure (i.e., dynamical form-factors) of neutral composites which plays an important role in providing consistency of the NCFT. An especially interesting case is that for a magnetic field configuration with the maximal number of independent nonzero tensor components. In that case, we show that the NCFT are finite for even $d$ and their dynamics is quasi-(1+1)-dimensional for odd $d$. For even $d$, the NCFT describe a confinement dynamics of charged particles. The difference between the dynamics in strong magnetic backgrounds in field theories and that in string theories is briefly discussed.