By no means do I have the mathematical background to understand most of the math used in elementary particle physics.

My current knowledge is of all the elementary particles and how they interact and build upon each other to build the macroscopic world.

Will I be able to continue forward and understand more in particle physics or should I stop now and start learning probability theory and whatever else I might need?

Is there a place where I can start to learn the maths? Is there a place where I can learn all the maths but on a novice level?

The coolest thing I have seen/understood is how the electromagnetic force works: Photons bounce back and fourth between particles in atoms creating the force field. So the thing that keeps my hand from going through the keys as I type is the electromagnetic force, specifically photons (please correct me if I am wrong about any of this).

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    $\begingroup$ To understand paricle physics, you need knowledge of group representation theory and Lie groups. $\endgroup$
    – user774025
    Apr 1, 2013 at 15:27
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    $\begingroup$ The Nobel winner in particle physics Gerard 't Hooft has compiled a list of essential subjects, with resources, which are required (pretty much in order) to get to research level in modern particle physics/quantum field theory/string theory. $\endgroup$
    – Michael
    Apr 1, 2013 at 15:30
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/16814/2451, physics.stackexchange.com/q/40754/2451 and links therein. $\endgroup$
    – Qmechanic
    Apr 1, 2013 at 15:41
  • $\begingroup$ Wow, I possibly went exactly backwards for Gerard't Hoofts lists. Might be where most of my misunderstanding comes from.. $\endgroup$
    – KDecker
    Apr 1, 2013 at 15:56
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    $\begingroup$ My gosh this guy hits my situation on the head. I've been looking for that for over two years I think. I feel like golem stumbling upon his precious for the first time. $\endgroup$
    – KDecker
    Apr 1, 2013 at 15:59

2 Answers 2


I don't think it is possible to learn physics without math. Mathematics is the language of physics and you can't learn a subject without learning its langauage. (This is just my opinion though).

To start with particle physics, I think you should first learn quantum mechanics and special relativity. For quantum mechanics, grab a copy of Griffith or any other similar book. Knowledge of single variable calculus and differntial equation is needed though.For vector calculus, you can look into the first few chapters of Feynmann lectures vol 2. Along with these, you must also learn abstract Linear algebra (theory of vector spaces) , very basic group theory (definition of group and group actions) and multivariable calculus.

Once you are done with qm and special relativity, you will be ready for Quantum Field Theory.A nice book for QFT is Quantum Field Theory in nutshell by A. Zee. Also,, now you should learn about theory of group representations and lie groups. A good introductory book for this topic is Group and Symmetries by Yvette Kosmann-Schwarzbach. The last chapter deals with particle physics.

Note that this route won't make an expert on the topic but you will gain a good understanding of it.

  • $\begingroup$ I never expected any understanding without math, I just wanted to know if my current understanding is enough for what I want to know. And it is close $\endgroup$
    – KDecker
    Apr 1, 2013 at 18:07
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    $\begingroup$ +1 for Zee. It won't by itself equip you to do some of the tough calculations, but the pedagogy is very clear and the level is just right for the most accessible introduction to QFT which doesn't lie through omission of essential math. The group theory appendix in Zee has the minimum you need to know - you pick most of that up through osmosis anyway. Groups are essential to physics, but mostly at a low level compared to mathematicians. A full mathematical course in group theory is rarely needed. $\endgroup$
    – Michael
    Apr 2, 2013 at 1:27
  • $\begingroup$ Is it possible to learn QFT without knowledge of classical mechanics, complex analysis, electromagnetism, partial differential equations, Green's functions, particle physics? $\endgroup$
    – auxsvr
    May 11, 2014 at 13:16

I believe that particle physics is a field where to be able to contribute to the field you must have the mathematics. Without them your understanding will be severely limited and in many cases not even wrong. On the other hand it is possible to contribute to physics to in general with no more math than you get in junior high. This is because physics is the study of everything that exists, and the relationships of all these things. To do physics all that is required is curiosity about the way things work and why. Albert Einstein kept pictures of Newton, Maxwell and Faraday on his study wall and Faraday knew only simple algebra yet is considered to be one of the "greats of physics".


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