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Cited by 4,275Particle physics theoretical and experimental studiesQuantum Chromodynamics and Particle InteractionsQuantum and Classical Electrodynamics

Axial vector vertex in spinor electrodynamics

Adler, Stephen L.·1969·Physical Review
DOI 10.1103/physrev.177.2426
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Abstract

Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closed-loop "triangle diagrams," the divergence of axial-vector current is not the usual expression calculated from the field equations, and the axial-vector current does not satisfy the usual Ward identity. One consequence is that, even after the external-line wave-function renormalizations are made, the axial-vector vertex is still divergent in fourth- (and higher-) order perturbation theory. A corollary is that the radiative corrections to ${\ensuremath{\nu}}_{l}l$ elastic scattering in the local current-current theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under ${\ensuremath{\gamma}}_{5}$ tranformations, the axial-vector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axial-vector current (PCAC) for the neutral members of the axial-vector-current octet…

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Crossref · 10.1103/physrev.177.2426

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  • Several defining physical properties of Weyl fermions, such as the chiral anomaly, continue to hold in the nonrelativistic condensed matter context.

    “Remarkably several of the defining physical properties of Weyl fermions, such as the so-called chiral anomaly, continue to hold in this nonrelativistic condensed matter context.”

    From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Adler, 1969

  • A single Weyl fermion coupled to an electromagnetic field results in the nonconservation of electric charge.

    “The chiral anomaly discussed by Adler-Bell-Jackiw (Adler, 1969; Bell and Jackiw, 1969), is an example of a quantum anomaly which in its simplest incarnation demonstrates that a single Weyl fermion coupled to an electromagnetic field results in the nonconservation of electric charge.”

    From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Adler, 1969

  • The chiral anomaly is associated with Weyl fermions.

    “Perhaps the most primitive example is the so-called chiral anomaly associated with Weyl fermions23456.”

    From Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal (2016) · cites this paper as [3]

  • Separated Weyl nodes are topologically stable because any perturbation respecting translational symmetry can shift but not annihilate them.

    “Separated Weyl nodes are topologically stable [19,20] because any perturbation respecting the translational symmetry can shift but not annihilate them [21,22].”

    From Experimental Discovery of Weyl Semimetal TaAs (2015) · cites this paper as [22]

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Authors
Adler, S. L.
Affiliations
Institute for Advanced Study (US)
Corresponding author
Adler, Stephen L.
ORCID
Adler, Stephen L.
Venue
Physical Review
Publisher
American Physical Society (APS)
Published
1969-01-25
Volume
177
Issue
5
Pages
2426-2438
ISSN
0031-899X (ISSN-L)
DOI
10.1103/physrev.177.2426
OpenAlex
W2223420584
Cited by
4,275
References
0
Citations by year
2026: 86 · 2025: 133 · 2024: 118 · 2023: 150 · 2022: 138 · 2021: 174 · 2020: 161 · 2019: 189 · 2018: 174 · 2017: 150 · 2016: 160 · 2015: 100 · 2014: 92 · 2013: 85 · 2012: 88
FWCI
42.04
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical Review (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
Keywords
spinor electrodynamics, triangle diagrams, Ward identities, wave function renormalization, fourth-order perturbation theory, radiative corrections, partial conservation of axial-vector current, two-photon decay, pion decay, eta decay

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