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  • Writer's pictureAlex Cassem

Update: quantum cosmology and not-so nutshell strings

It has been quite some time since I last made a post on my blog, and well there is some good reasoning for this. For one, I needed a break over the time period known to others as, ''winter break.'' And then I got tied up in school, setting up tutoring services for this spring semester; along with some math coursework (abstract algebra, mathematical foundations (ya know, the one that you are suppose to take before real analysis... that I took last semester, and abstract... which I am taking now), and probability). I also started a new research project here on campus involving another student and myself (sometimes other students stop by to learn and see what we are doing) and two professors: one from the math department, and one from the physics department. This I am really excited about since it is cross-department research, and I am starting to draw more people into theoretical physics among a student population that is largely industry and, shall we say, ''practical,'' in nature. But, here we are, working on quantum cosmology.

Yep, the project we are working on is learning the ins-and-outs of quantum cosmology. The student with me had zero knowledge on general relativity/quantum mechanics, but they most certainly have the math, so catching them up with the topics has been relatively easy, which was done this December and January. However, we have different interests within quantum cosmology: they love chaotic systems, so they are working on the BKL-singularity while I am working on more foundational questions and string theory. However, I want to try a quick calculation within the typical framework of quantum cosmology (canonical method with the Wheeler-DeWitt equation). Consider the Lagrangian, L = R - (1/4)F^2, which is the typical action for an electromagnetic field (U(1) field) on spacetime. (For the time being, do not consider the local-gauge term that we would need, and then would have to convert all covariant derivatives to covariant-gauge derivatives.) Then, find the EOM, and plug in the typical metric for the FRWL-metric and find the EOM based on this metric. Then, perform the usual quantization method for quantum cosmology of, a(t) --> d/da (think momentum operator), and see what pops out. Now, the whole goal is to mirror the calculation done for determining the expansion rate of a radiation dominated era with \rho ~ a(t)^4. It would be interesting to see if we can recover the same dynamics, but with either quantum corrections up to a limit, or if we have to perform some new tricks to understand this part/era of the universe.

I am also still working on my swampland research, but the details are becoming extremely technical since I am at the point of trying to construct what seems like a "physical-proof" for Riemannian moduli/geometry in the swampland and whether or not in general, given that they omit a fixed point that correlates to an infinite tower of states (or could signal to it). The issues I am having are the physical reasoning, but am reading a lot of no-go theorems for "inspiration."

The biggest update though is that I have done some of the problems in chapter 3 and 4 of Strings in a Nutshell text that I have been working on for a while (not all, since there are 70 problems in chapter 4)! Now, let me tell you first hand, the title of the textbook is misleading, almost a farce, since the chapter on conformal field theory can not be put into a nutshell! Oh, I still enjoyed it, but found a rather helpful book that I shall only denote as "the yellow pages," (the references are at the end of the solutions. The solutions are right here:

strings nutshell solutions ch 1-4
Download PDF • 375KB

Otherwise, I am still waiting on decisions (hopefully a very big one soon) for where to go for graduate school! But let me say, I wasn't on pins-and-needles on waiting for responses before last week, but after attending a certain open house... I am. I never thought I would have a chance, and now that it appears I have one to get into this specific school... I really believe I am a great fit for the school (holography plus cosmology plus strings plus......).

Have a great week, fingers crossed on graduate school acceptances for everyone out there!

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