The assignment was to read chapter 0 of our textbook (QFT for the Gifted Amateur) and then to hand in a note with the top two topics that you would like to review from that chapter.

The winning topics were Lorentz/Poincaré symmetry (lumping together related things like 4-vectors, tensors, etc…) and Fourier transformations. These are great choices!

There were also some questions inspired by the subsection “What is a field?” I think it’d be great to talk about these questions, but I’m going to save that for another time, or perhaps for a write-up on the course blog.

In our review class today (1/26/18), I’ll do some Fourier transform review, with an eye toward applying it to QFT in particular. I’ll be fairly light on the underlying intuition, but you can find a wonderful discussion that should really help here:

https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/

By the way, I can’t recommend betterexplained.com highly enough! The people putting that site together have done a marvelous job.

I will do some review of special relativity, probably during next week’s review class (Fri, Feb 2). That said, one question/topic request had to do with choices of metric signature. The two competing choices are the East Coast convention \((-,+,+,+)\) and the West Coast convention \((+,-,-,-)\). People get pretty passionate about which one is the “correct” choice. My sympathies lie with the East Coast convention (I’m a New York City boy, after all!), mainly because I think it’s simpler to deal with one minus sign than three (it also extends more easily to higher spatial dimensions since no new signs are introduced).

Despite my personal preferences, its common for particle physics and QFT books to use the West Coast convention. I think that if there is a reason other than just blind tradition, then it is likely due to the fact that the 4-momentum squared is proportional to rest-mass squared in this convention rather than negative rest-mass squared. Folks probably find that negative sign annoying, and if you’re doing lots of calculations involving four-momenta, it may be more practical to go this route.

For an amusingly high-minded argument for the superiority of the East Coast convention, take a look at:

http://www.math.columbia.edu/~woit/wordpress/?p=7773

Most folks agree that these things are called conventions since there isn’t a truly correct choice between them. But Woit makes a good case for going with the East Coast convention that goes beyond simple convenience.