Topology of the momentum space, Wigner transformations, and a chiral anomaly in lattice models
- Authors: Zubkov M.A.1,2, Khaidukov Z.V.1
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Affiliations:
- Alikhanov Institute for Theoretical and Experimental Physics
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 106, No 3 (2017)
- Pages: 172-178
- Section: Methods of Theoretical Physics
- URL: https://journals.rcsi.science/0021-3640/article/view/160477
- DOI: https://doi.org/10.1134/S0021364017150139
- ID: 160477
Cite item
Abstract
Lattice models that can be used to discretize the quantum field theory with massless fermions have been discussed. These models can also be used to describe Dirac semimetals. It has been shown that the axial current for general lattice models should be redefined in order for the usual expression for the chiral anomaly to remain valid. In this case, in the presence of a time-independent potential of the external electromagnetic field, the formalism of Wigner transformations allows relating the divergence of the axial current to a topological invariant in the momentum space that is defined for a system in equilibrium and is responsible for the stability of the Fermi point. The evaluated expression is the axial anomaly for general lattice models. This expression has been illustrated for models with Wilson fermions.
About the authors
M. A. Zubkov
Alikhanov Institute for Theoretical and Experimental Physics; Moscow Institute of Physics and Technology (State University)
Author for correspondence.
Email: zubkov@itep.ru
Russian Federation, Moscow, 117259; Dolgoprudnyi, Moscow region, 141701
Z. V. Khaidukov
Alikhanov Institute for Theoretical and Experimental Physics
Email: zubkov@itep.ru
Russian Federation, Moscow, 117259
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