The hardest part of research is to overcome one’s ego and know when one’s ideas are leading nowhere. Also, to accept advice from others.
It turns out that all that I have been doing for the past few weeks has been slightly off-track. Back to the main source: Alday and Maldacena.
Every single day I find stuff I would like to learn more about during the coming summer. Last year I pretended to learn general relativity and quantum field theory. I only got around to learn the basics. It was not enough, in my opinion, but I was very distracted and not motivated.
This summer is going to be different. Well, it has to be. Or else I am really done. Besides working on my research (more on that later), I want to learn about stuff. Stuff like what? A fair topic is supersymmetry and supergravity. During this semester I saw a bit of supersymmetry in the advanced field theory class. That was fun, but I feel like I still need more “practice”. My plan is to go through GGRS’ book Superspace. I still do not know how much, but I want to cover some of the quantum calculations in supergravity.
Something I wish to understand in more detail is the quantization of gauge fields. I saw some particular gauges this semester, but I want to learn more about the Faddeev-Popov construction and everything that comes with gauge fixing. That means learning more about BRST symmetry. I also wish to understand better the background gauge method. Also, I need to learn some renormalization. For all these I guess I will use some of the text books I have plus copies of the lecture notes I got from last year’s AQFT course taught by van Nieuwenhuizen.
Finally, and this is for fun, I want to learn more about monopoles in gauge theories. For that I think I will go with Harvey’s notes on the arXiv. This is all very ambitious, and it is pretty bad since at the end of the summer I only accomplish a fraction of all these and it looks small.
Oh, and maybe some string theory.
Here are some topics I want to learn more about (and some I want to really understand) during the summer:
- BRST symmetry
- renormalization of gauge theories
- supersymmetry and supergravity
- some string theory (whatever I need to learn more about the AdS/CFT correspondence)
- general monopoles
- some fancy mathematics
Hopefully this list will motivate me to write something about each topic on this list.