What are the key concepts needed to understand QED and QCD?

[Andreol263]

Hi physicists , I'm in high-school yet, and since I've started study physics for myself my aim is to understand more complex fields of physics, and one of these fields in QED(Quantum Eletrodynamics) and QCD(Quantum Chromodynamics), could anyone tell me what the path to go for a good basis for start learning these disciplines? Thank you all.

 

[Bong_Nebula]

What you'll really need is immense patience. QED and QCD take a lot of prerequisite knowledge. These are topics people don't really get into until (typically) senior year of their physics major, or graduate school. It's important to remember that. Don't put the cart before the horse.

As far as setting yourself to be well prepared once you get there, here is my recommendation:
Start with the math and elementary classical physics. If you try to skip steps you'll end up frustrated and confused.
Math you'll need:
-what ever you need to bridge your gap between what you know now and calculus
-calculus, single AND multivariable/vector calculus
-differential equations
-linear algebra
-some abstract algebra
-random bits of other fields like statistics and complex analysis (but these concepts are often self-contained in physics texts)

Physics:
go through some introductory classical mechanics book, and some introductory electromagnetism book. Make sure you can solve most of the problems - make sure you truly understand before moving on. After that, you can work your way through a modern physics text. My personal favorite is Modern Physics by Harris. It is very easy to self teach from. After that, you can starting getting into upper level quantum mechanics and electrodynamics. Then you'll be ready for QED and QCD.

This will literally take years, and (I don't mean to be discouraging because your enthusiasm is great, but,) nigh impossible on your own. My recommendation is to start it slow and deliberate so that by the time you get to university, you're very well prepared to study the advanced stuff with the help of experts.

 

[Andreol263]

Thank you so much for the reply, 3 years ago I've started study basic calculus, and now i have already studied ODE, Multi/Vector Calculus, Linear Algebra,and other little things, I'm reading Boas' book right now, i have read Introduction to Eletrodynamics(until chapter 4, because unfortunately occurred some 'problems' on my personal life), but what I'm really worried is things like theory of groups, functional analysis, lie algebra, and etc., these things scary me!, what i really need is some help in the understanding of this mathematics, so I'm going to rebuild my question, could you tell which mathematics should i learn other than that I've already specified above to have a fluid understanding of the topics? thank you in advance

 

[one]

Don't be scared of mathematics! It's actually fun :)
My mindset reccomendation not to learn mathematics just because you need it for physics, but to learn it because you enjoy it.

A good place to start is with logic and set theory since they are fundamental in the workings of modern mathematics.
Another suggestion is to take a closer look at calculus, from a more analytical perspective. This leads naturally into more abstract developments.

When you are learning the basics, it helps to move patiently and develop a clear understanding of why concepts are meaningful. Once you are comfortable with preliminaries, the more specialized topics are not so intimidating.