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.
I gave a talk on this at Nicohl Furey’s seminar Algebra, Particles and Quantum Theory, and you can see a video of my talk here:
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!
You can see my slides and more notes here.
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.