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 () to strings () and membranes that trace out -dimensional surfaces in spacetime (). The concept of "-velocity". The canonical -form on the extended phase space , where 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 “-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.