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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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To understand paricle physics, you need knowledge of group representation theory and Lie groups. –  user774025 Apr 1 '13 at 15:27
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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. –  Michael Brown Apr 1 '13 at 15:30
    
Possible duplicates: physics.stackexchange.com/q/16814/2451, physics.stackexchange.com/q/40754/2451 and links therein. –  Qmechanic Apr 1 '13 at 15:41
    
Wow, I possibly went exactly backwards for Gerard't Hoofts lists. Might be where most of my misunderstanding comes from.. –  BumSkeeter Apr 1 '13 at 15:56
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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. –  BumSkeeter Apr 1 '13 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.

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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 –  BumSkeeter Apr 1 '13 at 18:07
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+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. –  Michael Brown Apr 2 '13 at 1:27
    
Is it possible to learn QFT without knowledge of classical mechanics, complex analysis, electromagnetism, partial differential equations, Green's functions, particle physics? –  auxsvr May 11 at 13:16

Nope.

Physics, by definition, is the subset of Mathematics which pertains to our universe.

By the way, I assume that by "Particle Physics", you mean "Quantum Field Theory", Relativistic Quantum Mechanics applied to (quantum) fields.

My current knowledge is of all the elementary particles and how they interact and build upon each other to build the macroscopic world. I am just starting into trying to understand the forces and how they work. I just now a few days ago understand why nucleuses don't blow apart (residual forces).

Well, to learn even this much properly, you'll need to learn much more mathematics.

Assuming you already know Khan Academy level maths, you'll have to learn some

  • Matrix Calculus

  • Partial Differential Equations

  • Group Theory and Abstract Algebra

  • Exterior Algebra and more generally, Clifford Algebras

  • Tensors and Riemannian Geometry

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

Just learn the Khan Academy level maths and the above mentioned topics. And a lot of physics pre - requisites like:

  • Newtonian Mechanics

  • Lagrangian Mechanics and Hamiltonian Mechanics

  • Special Relativity

  • General Relativity (not compulsoury, but to get the intuitiion behind quantum field theory)

  • Matrix Quantum Mechanics and Schrodinger's wave Quantum Mechanics

  • Path Integrals

  • (Special) Relativistic Quantum Mechanics; Klein-Gordon, Dirac, Weyl Equations

  • Some Quantum Electrodynamics (Well, arguably, this is a part of Quantum Field Theory)

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?

Why'd you want to learn it at a novice level? With that, you'll learn nothing.

Anyway, see this list().

Quick note/question/insight into my knowledge level: The coolest thing I have seen/understood is how the electromagnetic force works. (please correct me if I am wrong) Photons bounce back and fourth between particles in atoms creating the force field?

Qualitatively, the answer is "whatever, I guess that I could say, yes." but Quantitatively, the answer is honestly just nothing but a "nonsense.". So just learn the math.

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"Physics, by definition, is the subset of Mathematics which pertains to our universe." I disagree with this. There's plenty more to physics than just pure math. I tend to agree more with Vladimir Arnold that the containment is in the other direction: "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap." –  Logan M Sep 22 '13 at 8:17
    
@LoganM: My point is that Physics needs experiments only because it's the mathematics that pertains to our universe; i.e. to find out if the mathematics we've done pertains to our univverse, or Mr Tom Dick Harry's. –  Dimensio1n0 Sep 22 '13 at 8:23
    
I like to think that experimentes are also necessary, besides the reason you just gave, when the maths are too hard to solve exactly: the experiment tells us whether the approximations or simplifying assumptions we used are valid or not. Or even an experiment can be used to find the answer to the maths: I always tell my students that one way to calculate a definite integral is to make a cardboard model, throw darts at it, count the number of hits and misses...etc.... or even just weigh the cardboard, for crying out loud... –  joseph f. johnson Nov 22 '13 at 3:55

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