Strongly Interacting Matter in Magnetic Fields pp 261-294

Part of the Lecture Notes in Physics book series (LNP, volume 871) | Cite as

The Chiral Magnetic Effect and Axial Anomalies


We give an elementary derivation of the chiral magnetic effect based on a strong magnetic field lowest-Landau-level projection in conjunction with the well-known axial anomalies in two- and four-dimensional space-time. The argument is general, based on a Schur decomposition of the Dirac operator. In the dimensionally reduced theory, the chiral magnetic effect is directly related to the relativistic form of the Peierls instability, leading to a spiral form of the condensate, the chiral magnetic spiral. We then discuss the competition between spin projection, due to a strong magnetic field, and chirality projection, due to an instanton, for light fermions in QCD and QED. The resulting asymmetric distortion of the zero modes and near-zero modes is another aspect of the chiral magnetic effect.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of PhysicsStony Brook UniversityStony BrookUSA
  2. 2.Physics DepartmentUniversity of ConnecticutStorrsUSA

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