2025/06/05 by Xavier, Praveen D., Zubkov, M. A.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2506.05066
We consider the chiral anomaly for systems with a wide class of Hermitian Dirac operators Q in 4D Euclidean spacetime. We suppose that Q is not necessarily linear in derivatives and also that it contains a coordinate inhomogeneity unrelated to that of the external gauge field. We use the covariant Wigner-Weyl calculus (in which the Wigner transformed two point Greens function belongs to the two-index tensor representation of the gauge group) and point splitting regularization to calculate the global expression for the anomaly. The Atiyah-Singer theorem can be applied to relate the anomaly to the topological index of Q. We show that the topological index factorizes (under certain assumptions) into the topological invariant (1)/(8π2)∫ tr(F\wedge F) (composed of the gauge field strength) multiplied by a topological invariant N3 in phase space. The latter is responsible for the topological stability of Fermi points/Fermi surfaces and is related to the conductivity of the chiral separation effect.