Relativistic field theories in a magnetic background as noncommutative field theories

Abstract:
I discuss the connection of the dynamics in relativistic field theories in a strong magnetic field with the dynamics of noncommutative field theories (NCFT). As examples, the Nambu-Jona-Lasinio model, quantum electrodynamics and quantum chromodynamics in a magnetic field are considered. It is shown 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 these NCFT. The NCFT could find interesting applications in condensed matter systems and string theories.