Chiral anomaly without relativity

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Science  23 Oct 2015:
Vol. 350, Issue 6259, pp. 378-379
DOI: 10.1126/science.aad2713

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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.