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MATHEMATICAL WORDS PART 1

“ANOTHER DAY with No Use for Calculus” reads a humorous, if inaccurate, t-shirt slogan. In fact, calculus is the mathematics of analyzing motion. So, in a sense, unless you’re utterly static, your life does involve calculus, not to say other math as well.

This became came particularly evident to me because of five article titles in Science magazine, September 20, 2019. I don’t pretend to understand the physics described in any of them, but I’m fascinated by how seemingly “theoretical” math has application in the real world today. Or at least the real world of modern science.

Here, in Parts 1 and 2 today and tomorrow, are tidbits not on the topics themselves, but rather on the associated math.

“Weyl”ing Away Time-Reversal Symmetry. Eduardo H. da Silva Neto’s article discusses precise band-structure measurements identifying two ferromagnetic Weyl semimetals. Which, alas, loses me already in the article’s subhead.

But I recognize the name Weyl as an influential twentieth-century mathematician.

Hermann Klaus Hugo Weyl, 1885–1955, German mathematician, theoretical physicist, and philosopher.

Weyl was one of the first to combine Einstein’s general relativity with nineteenth-century laws of electromagnetism. In 1929, Weyl proposed the concept of a fermion, a massless quasiparticle carrying an electric charge.

“Such quasiparticles,” Wikipedia notes, “were discovered in 2015, in a form of crystals known as Weyl semimetals, a type of topological material.”

Topology, by the way, studies properties that are preserved under continuous transformation. The oft-cited example is a donut and a coffee cup being topologically equivalent: Each has precisely one hole.

Discovery of Topological Weyl Fermion Lines and Drumhead Surface States in a Room Temperature Magnet. Ilya Belopolski and several of his colleagues are at the Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University. In their Abstract, they note “On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence.”

“Weyl”ing away with a Co2MnGa magnet. Image from Science, September 20, 2019.

“Our experimental results,” they conclude, “suggest a rich interplay of strongly interacting electrons and topology in quantum matter.”

Tomorrow in Part 2, this interplay of physics and mathematics continues, though, to the best of my knowledge, no t-shirts are involved. ds

© Dennis Simanaitis, SimanaitisSays.com, 2019

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