# How much Maths does one need in Particle Physics?

1. Sep 24, 2011

### MarcAlexander

Hi, I'm Marc. I'm 14, from the UK and I love Particle Physics and Nuclear Physics. I was just wondering about how much Maths and what areas of Maths I would need to accumulate the knowledge for, in order to do A-level and eventually University Physics, specifically Particle Physics.

Could anyone shed some Photons on my situation?

2. Sep 24, 2011

### Pythagorean

the field theory has classical roots in differential equations (which follows from calculus), the quantum mechanical part of it is mostly group theory and linear algebra (matrices and eigenstuffs).

3. Sep 24, 2011

### nickbob00

If you do maths GCSE and get an A, then do A level Maths and get an A, that's all the maths you need to get in to an undergraduate course. Ideally, you would do A level Further maths and also do additional maths GCSE or something like that, if it is offered at your school. At 14, you don't need to be teaching yourself much.

On an undergrad physics degree, you will do lots and lots of maths, much of which will be required rather than optional.

4. Sep 24, 2011

### MarcAlexander

Well I'm just wondering if Chemistry is more my thing. :\

You see, I'm personally very interested in particles, their sub-atomic particles, their elementary particles and so on. I have reason to believe this area of Science comes under Particle Physics. My dilemma is that I:
1) Don't really care about the rest of Physics besides the particle aspect, e.g.I couldn't give a damn about light refraction or thermal conduction.
2) I'm not a great fan of 'pointless' Maths, if you get were I'm coming from.

I'm starting to think maybe it's Chemistry I should be loured towards as that's pure particles with the odd metamorphic rock or two. Also I enjoy writing and reading Chemical formulae as it is short and simple. But my dilemma is that Chemistry seems to be more about how the atoms bond to form molecules rather than matter and anti-matter.

Physics or Chemistry??

5. Sep 24, 2011

### Awesomesauce

"The best of the golds at the bottom of the barrels of crap" - Randy Pausch
The 'rest of physics' does not come optional (un)fortunately. You can't just jump into the deep end without teaching yourself to tread water.

6. Sep 24, 2011

### MarcAlexander

It's not that I find the rest of Physics wrong, it's just I have no particular interest in them. I guess I'm just going to have to learn all the 'crap' in order to reach the 'gold'.

Thanks guys.

7. Sep 24, 2011

### Functor97

You do realise that those fundemental particles are pieces of "pointless" mathematics? No one can draw or see an electron let alone a quark... The more fundemental you go, the more mathematical it gets.

8. Sep 24, 2011

### MarcAlexander

You could see an electron or quark under an electron-microscope. But I acknowledge your point.

9. Sep 24, 2011

### Kevin_Axion

No, you can't. And I think the play on words is alluding to the fact that fundamental particles are points, and also QFT plays on group theory (abstract algebra), partial differential equations, differential geometry/topology etc.

10. Sep 24, 2011

### MarcAlexander

Could you explain to me what QFT is? I know what it stands for: Quantum Field Theory. I just don't know what relevance it has in Particle Physics, like S=D/T has in calculating velocities based on the distance and the time it took them to accomplish that distance. What does QFT tell us or prove to us?

11. Sep 24, 2011

### Kevin_Axion

I'll go through it really quickly since I have to go:

1. First we begin with classical mechanics and that includes Newtonian, Lagrangian and Hamiltonian mechanics. This field of physics studies the motion and dynamics of classical object i.e planets, balls etc. The objects follow trajectories in gravitational fields and can be modeled precisely in position and time.

2. Secondly we have relativistic mechanics. That is, the study of classical objects in high velocities or as $v\rightarrow c$. In this we are introduced to space-time or Minkowski space-time. We see that objects in an inertial frame experience time, distance and causality different then others.

3. Thirdly we have quantum mechanics, QM is the study of objects at the atomic level. Here, objects don't follow the rules of classical objects, everything has uncertainty. For instance there is an uncertainty between time and energy and an uncertainty between position and momentum etc. QM uses Hilbert spaces to define the state of a particle and uses non-commutative operators to describe uncertainty.

4. Now we have QFT. QFT is the combination of relativity and quantum mechanics and it forms relativistic quantum mechanics or the study of quantum mechanical objects in accelerated or inertial reference frames as $v\rightarrow c$. Here we see that the fundamental objects in nature are fields and particles are the local excitations of these fields. This is the most accurate depiction of nature so far.

12. Sep 24, 2011

### BloodyFrozen

:grumpy:

Much of physics requires MATH

MATH IS APPARENTLY THE LIFE.

13. Sep 24, 2011

### MarcAlexander

Is Quantum Physics for Dummies a good book?

Also what would be a good(simple) book for Physics in Maths be?

14. Sep 24, 2011

### MarcAlexander

I apologise if i pulled a 'heart string'. What I meant was that throughout school I am constantly taught Mathematics that seems to have no practical use like Median, Prime Factors, HCF, LCM etc. Personally I love Algebra.

15. Sep 24, 2011

### BloodyFrozen

Yes, I agree that mathematics in Highschool may be boring, but learn it. And then study on your own

16. Sep 24, 2011

### MarcAlexander

I completely agree. I just wish I'd had an interest in Physics from the start; maybe I'd have tried harder with Maths but, I was only a kiddie back then, now I'm doing my GCSEs. Are there any books that teach everything about Maths from baby stuff to high level stuff which would ultimately prepare me for Quantum Mechanics? And would Calculus be necessary?
If so then what is Calculus?

I apologise for so many questions. It's just I have no one else to ask really.

17. Sep 24, 2011

### micromass

Yes of course calculus would be necessary. Calculus is one of the most important theories around and is absolutely fundamental if you want to study any science.

Calculus basically allows you to analyze continuous functions and graphs in an easy way. It allows you to find areas under graphs, volumes, rate of change. And it can be used to solve optimization problems.

18. Sep 24, 2011

### BloodyFrozen

Well, as micromass already explained, Calculus would be extremely useful, but you can either take it in your highschool (if they offer it) or learn it by yourself.

I recommend getting a good grasp in HS Algebra and Precalculus/Trigonometry. As for textbooks, I can't really say. You could always ask to borrow a Precalc/Alg II book from a school teacher. Nearly any would suffice. As for Calculus texts, I'd ask someone else.

19. Sep 24, 2011

### micromass

Start with the excellent book "Basic mathematics" by Serge Lang. It consist of everything you need to know of high school mathematics (not including calculus). If you're done with that, then perhaps take a light calculus book like "practical analysis in one variable" by Estep. After that, you should take a fun book like Spivak or Apostol.

20. Sep 24, 2011

### MarcAlexander

I've just purchased "Quantum Physics for Dummies" of Amazon.