There are ten ways that a substance can have symmetry under time reversal, switching particles and holes, both or neither. But this fact turns out to extend far beyond condensed matter physics! It’s really built into the fabric of mathematics in a deep way.

You can also watch another version, where I explain this stuff to my friend James Dolan:

I like the idea of being able to watch an official talk but also watch the speaker chatting about the talk with a friend. It gives another view of the material. I skim over stuff Jim already knows, explain things I didn’t have time to get into in the actual talk, and emphasize the things I don’t understand. And he points out lots more patterns lurking in the tenfold way!

This entry was posted on Sunday, February 12th, 2023 at 1:00 am and is filed under mathematics, seminars. You can follow any responses to this entry through the RSS 2.0 feed.
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Definitely, thanks! At first I called both unitary and antiunitary operators U, and then I realized I should give the antiunitary ones some other name.

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You need the word 'latex' right after the first dollar sign, and it needs a space after it. Double dollar signs don't work, and other limitations apply, some described here. You can't preview comments here, but I'm happy to fix errors.

I suspect a typo in the slide on Wigner’s Theorem in https://math.ucr.edu/home/baez/tenfold/tenfold_web.pdf

In the definition of antiunitary, you probably want another J instead of a U.

Definitely, thanks! At first I called both unitary and antiunitary operators U, and then I realized I should give the antiunitary ones some other name.