### Quantization and Cohomology (Week 16)

#### Posted by John Baez

This week in our course on Quantization and Cohomology we considered some fancier path integrals. Then, fortified by these examples, we returned to the more abstract issues this course is really about:

- Week 16 (Feb. 27) - More examples of path-integral quantization. The particle in a potential on the real line. The Lie-Trotter Theorem. The particle in a potential on a complete Riemannian manifold. Back to general questions: how do we get a Hilbert space from a category equipped with an action functor? The problem of Cauchy surfaces.

Last week’s notes are here; next week’s notes are here.

An interesting anecdote related to our discussion of Cauchy surfaces and (not mentioned in the notes) closed timelike loops.

I mentioned that Einstein and Gödel were friends at the Institute of Advanced Study in Princeton back in the 1950s. Gödel learned general relativity, and found a solution called the Gödel universe, where there’s a field of observers who each trace out closed timelike loops and each see the rest of the universe revolving around him — perhaps a subtle comment on life at the Institute. The interesting thing is that he did this just to provide evidence for his conviction that time might not be described by a partial ordering on the set of events!

One of the students replied with this anecdote: Rudy Rucker visited the Institute for Advanced Study and asked Gödel why the illusion of the passage of time is so convincing. Gödel replied something like "For me, it’s not".

## Re: Quantization and Cohomology (Week 16)

That’s a wonderful anecdote. And since I’m hearing it at least third-hand, on the Internet it must be true!