Update and Path Integrals
Good (morning/afternoon/evening/night)! It is currently 2:44am for me so I am not sure which one to type... It has been quite awhile, which I will blame on the semester ending which entails: lots of people need tutoring, final projects for courses, final exam studying, and miscellaneous items/objectives.
However, since we (college students) are on winter break now, I have had time to catch-up on some of my favorite topics, and of course question reality. I recently asked, ''does a photon feel drag,'' meaning that when a photon traverses in flat space, there is no interaction with the gravitational field, or the graviton. However, you would think that when a photon is moving along a curved geodesic, there is an interaction between the photon and graviton to ''keep it on the track'' which means interactions, which I would think, would make the photon appear to slow down. My initial thought is to attempt to derive the propagator (in the weak field limit) of a graviton, photon, and conjure-up an interaction term via the path integral method. However, I quickly realized I do not know everything that I would need to know about the path integral to solve this problem.... So, I decided to write notes/example problems/solutions on the path integral method used in quantum mechanics, quantum field theory, and even some problems I found in Polchinski's, String Theory Vol. 1, textbook dealing with the path integral. That is attached below.
I don't think I am finished with this resource/notes, but for now this is as far as I will take these notes.
So, this is all I have done so far during my winter break. I am also slowly doing proofs through a text on topology (it's by Mendelson, published by Dover), and setting up the research project which I have previously mentioned on quantum cosmology.
Other then this, the end of the semester when about as well as I could have hoped. Courses of course went great.... but, Real Analysis really started to take a toll at the end (I got a high B at the end, yet still a B). This is also why I am confident on going through the introductory text on topology.
Otherwise, that is all I have for now, so I hope you guys/gals have a great Christmas and happy New Year.