State-Observable Duality

It’s confusing having two blogs if you only have one life. I post about my work at the Centre for Quantum Technology here. I post about abstract algebra at the n-Category Café. But what do I do when my work at the Centre for Quantum Technology starts using a lot of abstract algebra?

I guess this time I’ll do posts over there, but link to them here:

State-Observable Duality (Part 1).

State-Observable Duality (Part 2).

State-Observable Duality (Part 3).

This is a 3-part series on the foundations of quantum theory, leading up to a discussion of a concept I call ‘state-observable duality’. The first part talks about normed division algebras. The second talks about the Jordan-von Neumann-Wigner paper on Jordan algebras in quantum theory. The third talks about state-observable duality and the Koecher-Vinberg theorem.

I think I’ll take comments over there, so our discussion of environmental issues here doesn’t get interrupted!

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