### Quantization and Cohomology (Week 7)

#### Posted by John Baez

Here are yesterday’s notes on Quantization and Cohomology:

- Week 7 (Nov. 14) - From particles to strings and membranes. Generalizing everything we’ve done so far from particles ($p = 1$) to strings ($p = 2$) and membranes that trace out $p$-dimensional surfaces in spacetime ($p \ge 0$). The concept of "$p$-velocity". The canonical $p$-form on the extended phase space $\Lambda^p T^*M$, where $M$ is spacetime.

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

Now we’re getting to the cool stuff: after reviewing classical mechanics, now we can *generalize it* from particles to strings and higher-dimensional membranes following Rovelli’s ideas on extended phase space. We’ll even go beyond his ideas in various ways, like introducing the concept of “$p$-velocity” (I don’t think he mentions that - I could be wrong) - and, much more importantly, relating all this stuff to categorification.

In this lecture, the fun begins.

## Re: Quantization and Cohomology (Week 7)

Just for the record:

Schuller and Wohlfarth did reformulate the Nambu-Goto action of the string in a way close in spirit to the last remarks about multivelocities in the above notes in their paper Canonical differential structure of string backgrounds.