Hi, everyone. My name is haowu, one of physics graduate students. I am interested in the quantum field. And there are lots of connection between topology and quantum field theory. Instanton as a topological solution would be my final project topic.
The instanton is the solutions When we solve field equation use Euclidean metric instead of Minkowski metric. Because of this, this solution is in the space-like region, where velocity is larger than the speed of light. Different solution corresponding to different winding numbers. A Careful examination of the instanton solution and its topological properties is the center of this project.
Nick
February 19, 2018 — 22:45
Instantons are a very cool subject, and conceptually a little weird, which I guess is half the fun! I would love to hear about the deformations topic from the colloquium. I didn’t get to go so if you left the choice up to me, I might be a little biased.
afranci2
February 19, 2018 — 22:09
All the topics seem interesting to me as your physics classmate. I didn’t know that neutrino oscillations have topological phase contributions. Is the phase in PMNS or CKM matrix has something to do with this topological phase. It might then be a good tool to study CP violation. Anyways its good to see the same thing in different math perspectives. Currently, I don’t have much idea about topology to see how topology is relevant here. So I am looking forward enthusiastically to your project.
caroyse
February 19, 2018 — 21:30
I’m in the second-semester of a Quantum Field Theory course, and have heard the word ‘topology’ thrown around with topics in QFT, but have never learned why or how. I’m curious- what is an instanton? and in what sense is it ‘a solution’? How does a ‘localized solution’ differ from a ‘normal solution’?
gljohns3
February 19, 2018 — 20:52
Neutrino oscillation would probably be super interesting in this context. I’m not sure exactly what is going on there, but there is a fiber bundle. From what you are saying, the fiber at each point in the field is flavor space. Then physics comes in when you add “motion” through the fiber bundle. In math you’ll need a connection but in physics it is a potential, which to me makes sense (so so) since a free particle doesn’t know how to move until you tell it the potential. But the potential (connection) moves the particle through space and through the fiber (like the neutrino oscillating). This stuff is kind of insanely overarching in physics, but maybe I’m just getting carried away. What I want to get comfortable is how geometry describes quantization rules.
brwendt
February 19, 2018 — 20:11
I am going to be honest and admit that I did not know what a lot of those words were. However, it is always interesting to hear how abstract math concepts and advanced physics concepts can be related, and it proves to me that just how interlaced into the world mathematics is. I’m sorry I can’t offer you any guidance on what direction to choose, but I think that it is awesome that you found solid, real life applications of the things we learn in class, and I hope that I can one day know as many big physics words as you.