The current title is a mouth full, but perhaps it is sufficient.
It is almost 2:00 PM as I write this and I have just finished ‘t Hooft’s paper on quantum field theory (QFT). This post is not as much as the content of the paper but how I went about reading the paper and how much I actually learned through this first read through. Now even if you don’t care about physics, this post will help you understand a technique I use when reading a piece of nonfiction.
All I did for this first read-through of ‘t Hooft’s paper is read the words, glance at the equations, and occasionally looked up some (but not all) of the terms I did not understand. I did not spend the time to carefully go over the derivations, nor did I spend the time carefully looking over the text make sure I understood everything. I did spend some time thinking about the equations, comparing them to ones I know in other fields, and thinking about the concepts and how they relate to my previous knowledge of QFT and other physics subjects. But the whole goal of this was to get through the paper and get a broad overview of the field so it can start to fester, grow, develop, into something more usable to me in the future.
This is what I did when I studied most of the textbooks I have read in physics, and many of the papers too. With the papers, you do not know if it will be useful, so you first read the introduction and conclusion and maybe look at some of the equations. Then if it seems useful, you can read the paper like I did to get a better understanding and see if it is worth more careful study. While time isn’t necessarily money in physics, there are only so many papers you can read so being able to sort through which ones are useful is important, and reading them like I just read ‘t Hooft’s is a process to determine if they’re important enough for you to take time for a more detailed look. If you will use those papers, you already have a sufficient understanding of the paper, so you know where the author(s) will go as you read through the paper again.
With textbooks this read through, that is slightly better than skimming, will be a good look before class so you can better follow along, or if you’re studying alone, it can be enough for you to start to glance at the problems and start to see what might be done to tackle them. You can then go through the text again with the problem in your mind and know where to look for help. As you do more problems and go back through the text, you will build up a stronger base and understand more of the text. Reading papers and textbooks is great, but the real core of physics is problems. Everything you’re reading in physics is just explanations of math problems that describe the world around us. S
Reading papers and textbooks is great, but the real core of physics is problems. Everything you’re reading in physics is just explanations of math problems that describe the world around us. Even in other fields the questions and problems that are asked are important as they guide you to areas that are probably the most useful to you as the reader (I am not discrediting the sidenotes as they can be useful, but once you have the base you can easily pile these pieces on). This is why I read this paper this way, so I can have an idea of what is going on, and now I can focus on the real meat and potatoes of physics, the equations. Yes, the paper explains various equations, but actually doing problems and working them out for yourself is the most important part.
I will skim through the paper a few times to pick up a few more morsels, but the next step is doing a bunch of problems while referring back to this paper (and other resources) to help with that important foundation. After tackling these problems, I will go back and soak up more information that explains some of the finer points coupled with more problem-solving.
So you have gotten to the end and may be asking yourself how much I truly gained from this. Well, quite a lot. Can I explain all that I read? No. Can I solve any problem I encounter? No. What I have is a bunch of bricks, a lot of new terms, the patterns to the equations, the steps of how to combine special relativity and quantum mechanics, an understanding of how the physics I already know relates to QFT, and more that my sleep-deprived brain is unable to remember (which is why I will skim through the paper before working on any problems).
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This post is part of a series on my journey through teaching myself Quantum Field Theory.
