Topology of generalized spinors and chiral anomaly
Abstract
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 $$\mathcal{d}$$ = 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.
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1598740
- Alternate Identifier(s):
- OSTI ID: 1800027
- Grant/Contract Number:
- FG0201ER41195; GP005704; FG02-01ER41195
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 4; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics
Citation Formats
Yee, Ho-Ung, and Yi, Piljin. Topology of generalized spinors and chiral anomaly. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.045007.
Yee, Ho-Ung, & Yi, Piljin. Topology of generalized spinors and chiral anomaly. United States. https://doi.org/10.1103/PhysRevD.101.045007
Yee, Ho-Ung, and Yi, Piljin. Mon .
"Topology of generalized spinors and chiral anomaly". United States. https://doi.org/10.1103/PhysRevD.101.045007.
@article{osti_1598740,
title = {Topology of generalized spinors and chiral anomaly},
author = {Yee, Ho-Ung and Yi, Piljin},
abstractNote = {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 $\mathcal{d}$ = 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.},
doi = {10.1103/PhysRevD.101.045007},
journal = {Physical Review D},
number = 4,
volume = 101,
place = {United States},
year = {2020},
month = {2}
}
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