Summer break is about to begin. And boy do I have a lot of work to do. Why, you ask? It is because I want to learn as much as I can while I still can. While running towards trying to know everything, I hope I am not leaving loopholes in my concepts. But that is the concern for another post.

I got accepted to the Summer Fellowship Programme- 2018, at IIT Madras. It was proably the best news I got this semester, as I felt directionless and was already wondering how to utilize my summer in a productive way. Yes, I am that kind of a guy, one who likes to plan things in advance (but might not necessarily follow them at the end). This fellowship allows me to work under the supervision of the esteemed faculty of the Department of Physics at IIT Madras for a period of 60 days. I don’t know what I am going to work on, but if asked, I’d liked to study the mathematical foundations of quantum mechanics. This would include studying about Hilbert spaces, why Hilbert spaces in quatum mechanics, formulation of quatum mechanics from its bare-bones, etc.

This brings me to the next plan for the summer. I will be reading up on functional analysis by myself this summer. I am planning to follow Kreyszig, which is both very popular and highly recommended. I would tell you about functional analysis but then I guess I should do that once I have actually read up on it so that I can tell you about my views instead of broadcasting what the general public thinks. Why functional analysis? Sticking to the point, because it will help me in understanding why Hilbert space and not any other space (or is there one?) is suitable for quantum mechanics. It is always good to know the math before you get into the physics. While this is not a widely accepted opinion, this is certainly how I feel about things.

Functional analysis will also help me in another thing I am pursuing on the side: loop quantum gravity. I started working on loop quantum gravity since the mid of this semester, and by working I mean reading up on things related to loop quantum gravity which will help me understand the basic philosophy and mathematics (which I think is the best definition of physics and I just came up with it, philosophy + mathematics, though I am sure it is a very common definition and I am not the first one to think about it, but it felt good when I did) behind loop quantum gravity. I am currently studying how to quantize a classical theory and how we did that to get our quantum theory. One thing that my supervisor has asked me to do for the summer related to this pursuit is to get acquainted with GNS construction. What is it? Why? All answers will be provided once I am done with it.

As I am writing this post, I have an increasing feeling of realization that I am being way too ambitious with my summer. Why? Because I have yet another objective for the summer. It is to learn quantum information and computing. Quantum mechanics has intrigued me for long and it will be fun to look at how it is applied to computing. To do the same, I signed up for an online course which is being conducted by a few of my batchmates and would love to follow their lead as they have already done a full-fledged course on the subject.

I guess that is all for this summer. I plan on reading Modern Quantum Theory by JJ Sakurai as well, maybe as something just before I sleep at night, or maybe during leisure, but I won’t add it as an objective as I am going to do it for the fun of it, given Sakurai’s is a really good book and I remember loving it the first time I started it but left it as it became too mathematical for me to handle. This was an year ago. Hopefully, that won’t be the case this time.