Scale Magnetic Effect in Quantum Electrodynamics and the Wigner-Weyl Formalism

Abstract

The Scale Magnetic Effect (SME) is the generation of electric current due to conformal anomaly in external magnetic field in curved spacetime. The effect appears in a vacuum with electrically charged massless particles. Similarly to the Hall effect, the direction of the induced anomalous current is perpendicular to the direction of the external magnetic field $\mathbf{B}$ and to the gradient of the conformal factor $\tau$, while the strength of the current is proportional to the beta function of the theory. In massive electrodynamics the SME remains valid, but the value of the induced current differs from the current generated in the system of massless fermions. In the present paper we use the Wigner--Weyl formalism to demonstrate that in accordance with the decoupling property of heavy fermions the corresponding anomalous conductivity vanishes in the large-mass limit with $m^2\gg |e\mathbf{B}|$ and $m\gg |\nabla \tau |$.

12 pages, accepted for publication in Phys.Rev.D

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• Precise Wigner-Weyl calculus for lattice models
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• Hall conductivity as topological invariant in phase space
• Discrete Wigner-Weyl calculus for the finite lattice
• Wigner - Weyl formalism and the propagator of Wilson fermions in the presence of varying external electromagnetic field
• Hall conductivity of strained $Z_2$ crystals
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
• Chiral anomaly in inhomogeneous systems with nontrivial momentum space topology