Nondecoupling phenomena in QED in a magnetic field and noncommutative QED

Abstract

The dynamics in QED in a strong constant magnetic field and its connection with the noncommutative QED are studied. It is shown that in the regime with the lowest Landau level (LLL) dominance the U(1) gauge symmetry in the fermion determinant is transformed into the noncommutative $U(1{)}_{nc}$ gauge symmetry. In this regime, the effective action is intimately connected with that in noncommutative QED and the original U(1) gauge Ward identities are broken (the LLL anomaly). On the other hand, it is shown that although a contribution of each of an infinite number of higher Landau levels is suppressed in an infrared region, their cumulative contribution is not (a nondecoupling phenomenon). This leads to a restoration of the original U(1) gauge symmetry in the infrared dynamics. The physics underlying this phenomenon reflects the important role of a boundary dynamics at spatial infinity in this problem.

arXiv comment7 pages, REVTeX4

References in corpus (8)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Dimensional Reduction and Catalysis of Dynamical Symmetry Breaking by a Magnetic Field
• Theory of the Magnetic Catalysis of Chiral Symmetry Breaking in QED
• Dynamical Chiral Symmetry Breaking in QED in a Magnetic Field: Toward Exact Results
• Relativistic field theories in a magnetic background as noncommutative field theories
• Large N dynamics in QED in a magnetic field

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• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory
• Noncommutative Electrodynamics from $SO(2,3{)}_{\star }$ Model of Noncommutative Gravity
• Towards Noncommutative Fuzzy QED
• Backward Compton Scattering and QED with Noncommutative Plane in the Strong Uniform Magnetic Field
• Nonlocal regularisation of noncommutative field theories
• Noncommutativity vs. Transversality in QED in a strong magnetic field