Hello, I am new in this forum. I studied physics up to the equivalent of a MSc. This included mainly QFT and GR. Then, instead of following a PhD, I went to finance. Now, after a few years, I have decided I want to go back and study QFT. Not full time, but part time (in my free time). I already know I am not intelligent enough to make important discoveries. What I want is to understand QFT in my own way.(adsbygoogle = window.adsbygoogle || []).push({});

I recall that what disturbed me in QFT (and in QM) was that I could not relate the concepts to mathematical structures. For me, it is necessary to relate concepts to mathematical concepts. But studying QFT was not done in this way: you study the Klein-Gordon, and Dirac, and QED quantization, and you see many tricks that pave the path to go fast and to the point: you can calculate. But when I studied, I could not reach to the point to relate all those concepts in mathematical form. I am sure that people more intelligent than me can do that, though.

Now I know (or at least, I have read about it), that all the stuff about operators, commutators and anticommutators have something to do with group and algebra representations. And that the Feynman-Kac theorem relates the functional analysis view (values of operators under some Hilbert space states) with the probabilistic view (eg, correlation functions). But almost always, in QFT books the functional analysis view is stressed, as opposed to the probabilistic view. I would like to develop the probabilistic view from scratch: I have my probability space, well defined, then I see the random variables, the martingales, the Radon-Nikodim theorem how is it applied, ... ie, I can study math books and then physics is only to use theorems, with the hypothesis taking some particular values.

Yes, I know that this is not a modern approach. I have read many good physicists saying that mathematizing physics to the extreme does not lead to good insights in Nature. But I do not want to have good insights in Nature. I just want to understand QFT my way.

Please, help!

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# How to start again with QFT?

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