Bringing order to the expanding fermion zoo

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Science  05 Aug 2016:
Vol. 353, Issue 6299, pp. 539-540
DOI: 10.1126/science.aag2865

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We observe space as a continuum, but we might entertain the thought that there is an underlying lattice and that space is actually a crystal. Which particles would inhabit such a lattice world? This question was first raised by Werner Heisenberg in 1930 in an attempt to remove the infinities that plagued the continuum quantum mechanics. His Gitterwelt (lattice world) hosted electrons that could morph into protons, photons that were not massless, and more peculiarities that compelled him to abandon “this completely crazy idea” (1, 2). Heisenberg's motivation to put electrons on a lattice came from solid-state physics, which in the 1930s was just developing as a field of research and which has now become a playground for “crazy ideas” from particle physics. In this spirit, on page 558 of this issue Bradlyn et al. (3) use concepts borrowed from crystallography to classify the electronic excitations of the lattice world, and then use that to identify possible candidates of materials where they become a reality as (nonfundamental) quasiparticles.