Topology of Generalized Spinors and Chiral Anomaly

Abstract

Weyl fermions with nonlinear dispersion have appeared in real world systems, such as in the Weyl semi-metals and topological insulators. We consider the most general form of Dirac operators, and study its topological properties embedded in the chiral anomaly, in the index theorem, and in the odd-dimensional partition function, by employing the heat kernel. We find that all of these topological quantities are enhanced by a winding number defined by the Dirac operator in the momentum space, regardless of the spacetime dimensions. The chiral anomaly in $d=3+1$, in particular, is also confirmed via the conventional Feynman diagram. These interconnected results allow us to clarify the relationship between the chiral anomaly and the Chern number of the Berry connection, under dispute in some recent literatures, and also lead to a compact proof of the Nielsen-Ninomiya theorem.

42 pages, 1 figure

References in corpus (10)

• Topological Field Theory of Time-Reversal Invariant Insulators
• The Chiral Magnetic Effect
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Topological response in Weyl semimetals and the chiral anomaly
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Charge separation induced by P-odd bubbles in QCD matter
• Topological spin transport of relativistic electron
• Chiral fermions as classical massless spinning particles
• Constructing phase space distributions with internal symmetries
• Dynamic chiral magnetic effect and Faraday rotation in macroscopically disordered helical metals

Cited by in corpus (4)

• Gauge Field Induced Chiral Zero Mode in Five-dimensional Yang Monopole Metamaterials
• Chiral anomaly in non-relativistic systems: Berry curvature and chiral kinetic theory
• Berry's phase and chiral anomalies
• Anomalous Chiral Anomaly in Spin-1 Fermionic Systems