Journal
PHYSICAL REVIEW D
Volume 101, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.101.045007
Keywords
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Funding
- U.S. Department of Energy, Office of Science, Office of Nuclear Physics [DE-FG0201ER41195]
- KIAS individual grant at the Korea Institute for Advanced Study [GP005704]
- National Research Foundation of Korea [PG005704] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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Weyl fermions with nonlinear dispersion have appeared in real-world systems, such as in the Weyl semimetals 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 literature, and also lead to a compact proof of the Nielsen-Ninomiya theorem.
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