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Relativistic field theories in a magnetic background as noncommutative field theories

E. V. Gorbar·V. A. Miransky
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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.

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E. V. Gorbar, V. A. Miransky. 2004-10-13. Relativistic field theories in a magnetic background as noncommutative field theories. https://doi.org/10.1103/physrevd.70.105007

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