Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-03-03
Phys.Rev. D72 (2005) 065014
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, REVTeX4, v2: clarifications added, v3: to match PRD version
Scientific paper
10.1103/PhysRevD.72.065014
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.
Gorbar Eduard V.
Homayouni Saeid
Miransky V. A.
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