Chiral Anomaly

Many thanks to Norman Page, the fermion equation is the chiral Dirac equation, e.g. UFT248 ff. and the fermion equation has been intensively studied. There should be no problem in addressing the chiral anomaly with the fermion equation. Readers are encouraged to address this problem on their own initiative.


Myron The full texts are paywalled Norman

Chiral anomaly without relativity

  1. Anton Burkov

+ Author Affiliations

  1. Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, and National Research University ITMO, St. Petersburg 197101, Russia.
  1. E-mail: aburkov


The Dirac equation, which describes relativistic fermions (like electrons moving at nearly the speed of light), has a mathematically inevitable but puzzling feature: negative-energy solutions. The physical reality of these solutions is unquestionable, as one of their direct consequences—the existence of antimatter—is confirmed by experiment. However, the interpretation of the solutions has always been somewhat controversial. Dirac’s own idea was to view the vacuum as a state in which all the negative energy levels are physically filled. This “Dirac sea” idea seems to contradict a common-sense view of the vacuum as a state in which matter is absent. On the other hand, the Dirac sea is a very natural concept from the point of view of condensed matter physics, as there is a direct and simple analogy: filled valence bands of an insulating crystal. There exists, however, a phenomenon within the context of relativistic quantum field theory, whose satisfactory understanding seems to be hard to achieve without assigning physical reality to the Dirac sea. This phenomenon, the chiral anomaly, presents a quantum mechanical violation of chiral symmetry; it was first observed experimentally in particle physics as a decay of a neutral pion into two photons. On page 413 of this issue, Xiong et al. (1) report the observation of this phenomenon in a condensed matter system—a crystal of Na3Bi—manifesting as an unusual negative longitudinal magnetoresistance; the vacuum/insulating crystal analogy is now all the more tangible.

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Evidence for the chiral anomaly in the Dirac semimetal Na3Bi

  1. Jun Xiong1,
  2. Satya K. Kushwaha2,
  3. Tian Liang1,
  4. Jason W. Krizan2,
  5. Max Hirschberger1,
  6. Wudi Wang1,
  7. R. J. Cava2,
  8. N. P. Ong1,*

+ Author Affiliations

  1. 1Department of Physics, Princeton University, Princeton, NJ 08544, USA.
  2. 2Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.
  1. npo

In a Dirac semimetal, each Dirac node is resolved into two Weyl nodes with opposite “handedness” or chirality. The two chiral populations do not mix. However, in parallel electric and magnetic fields (E||B), charge is predicted to flow between the Weyl nodes, leading to negative magnetoresistance. This “axial” current is the chiral (Adler-Bell-Jackiw) anomaly investigated in quantum field theory. We report the observation of a large, negative longitudinal magnetoresistance in the Dirac semimetal Na3Bi. The negative magnetoresistance is acutely sensitive to deviations of the direction of B from E and is incompatible with conventional transport. By rotating E (as well as B), we show that it is consistent with the prediction of the chiral anomaly.

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