Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-27
Phys.Rev. D70 (2004) 105007
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, REVTeX4, clarifications added, references added, to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.70.105007
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.
Gorbar Eduard V.
Miransky V. A.
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