# Math required for particle physics

#### Woozie

Im wondering if anyone could help me on what math to study for particle physics.

So far I have taught myself calculus (differential calc through vector analysis), differential equations (ordinary and partial), and I am currently studying linear algebra, and abstract algebra. I really want to study particle physics but I dont know what types of math I should study when I finish the algebra.

Also, is there any recommended physics or math books I should study? Any recomended websites?

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#### Norman

When you say particle physics, what level are you talking about? Are you thinking of studying from Griffiths Particle Physics or are you trying to learn the Quantum Field Theory known as the Standard Model? If you are starting with Griffiths, you have enough math. If you are looking to start learning Quantum Field Theory, you need to first learn classical field theory and quantum mechanics. Basically, a lot of people come here and ask similar questions. They always get replied to with more questions. And when they get an answer, it is still dependent upon on the poster assuming some things about what they think is the most important part. I say start where you think to start, and inevitably you will have to go back and study some math, (re)learn some physics that you missed or forgot. I say, just start where you think you should and if you get too frustrated or stuck, go backwards and learn the foundation or next step back of the physics properly.
Good luck.

#### Woozie

I am already studying at the level of griffiths but I wanted to know what math I should start studying to study things like the standard model and quantum chromodynamics.

Also, do you have any favorite math or physics textbooks that you think I should get? Finding good books is one of the biggest problems I have when trying to teach myself something.

#### Norman

Well you will need to be well versed in Quantum Mechanics and Classical Field Theory before you consider the QFT which you will need to learn before you start in on the Standard Model. If you haven't done any QM, some people think that Griffiths intro book on it is good. I think you might be better served with Shankar's book on QM. Once you have a good handle on QM and Classical Field Theory, some good QFT books are Ryder, Peskin and Schroeder, M. Guidry, and I J R Aitchison and A J G Hey. But I cannot stress enough that you will not be prepared for QFT without a very good grasp on QM, which can be very difficult to get on your own. For more book recommendations go to the academic advising forum and read the book recommendations.
Cheers.

#### samalkhaiat

You need one step further in math. IT IS GORUP THEORY, to be specific the theory of Lie groups & algebras. Poincare group (Lorentz's group SO(1,3) plus Translation), and the special unitary groups SU(n) (The gauge groups) are essential for studing QFT (The theory of particle physics).

GOOD LUCK

#### marlon

Woozie said:
Also, is there any recommended physics or math books I should study? Any recomended websites?

How about some advice from a Nobel Prize Winner in particle physics ?

regards
marlon

#### Moneer81

Woozie,

Just out of curiousity, are you seriously teaching yourself Quantum Mechanics and Particle Physics ???? If you are, then I am really impressed. I am going down the same road but I decided to go back and gain full mastery of classical mechanics, electrodynamics, and relativity. After that, I am gonna take a shot at QM. Not sure how successful I will be, but I am gonna heavily rely on this forum

Good Luck.

#### Woozie

I have lots of people asking am I really teaching myself this stuff. But you would be amazed by how many people on physicsforums teach themselves physics. Its really no big deal; theres no reason to be impressed with what I am doing. Anybody can do it if they really want to.

Im sure you will be successful at quantum mechanics. Its not as hard as you probably think. Some of my some college professors made it seem like teaching myself QM was going to be the hardest thing anyone could ever do. So far it hasnt been any harder than anything else I have studied, it just takes more time.

Also, you say that you are going to master classical mechanics, relativity, and electrodynamics. What books are you using for these subjects and do you think they are good books? I am probably going to a little more studying in these subjects because I dont really like the books I used to learn them in the first place. I have asked professors about recommended books. The books they recommend are good, but they usually either dont provide enough problems at the end of chapters or dont provide many solutions. A lot of the authors of textbooks assume that students will have an instructor to go along with the book and this puts the self teachers at a disadvantage. But then, I also tend not to like books written specifically for self teachers. If you have any books that you think are very good can you tell me the title, author, and edition?

#### Moneer81

Yeah I agree with you about books. I am constantly looking for good textbooks. For Classical Mechanics, I found this one that I fell in love with, called "Classical Mechanics" by John R Taylor. I think its a new book, its very easy to understand and the author explains everything real good and I think it should appeal to students of different backgrounds. I've used Marion's book before but this one (Taylor's) blows it out of the water. Highly recommended.

As far as electrodynamics, I've used Griffiths and everyone loves that book and I think its ok although I would like to see more details and examples. I am looking for a good EM book so if you know of any then just let me know. I think I am gonna attempt using Griffiths book again and maybe find a solution manual or something.

Relativity is an easier subject I think and I've seen many books or just selected chapters from certain books and most of them were satisfactory. If you're interested in a more thorough qualitative understanding of relativity and such concepts then you should check out "The Elegant Universe" by Brian Greene. I just started reading this book and I like it so far I think it is aimed at those with less mathematical knowledge but people like me and you will definitely appreciate the "english" description of those principles.

Any books that you recommend ?

#### Woozie

I actually am using a book by taylor for my lab class in college called intro to error analysis. He seems to be a good author so I will probably check his book out.

For classical mechanics I have no recomendations for books but I have some against books. Do not get analytical mechanics by Grant Fowles Unless you have another book with a lot of problems and solutions. See my review at

https://www.amazon.com/gp/product/A2UNMI6FGH/?tag=pfamazon01-20
(scroll down the page. its the second reveiw)

Also, you should go to amazon.com and write reveiws on books you have read.

For electicity and magnetism you should definetely get schaums outline of electromagnetics. I dont know if your familiar with schaums outlines but they are basically books with lots of really good problems and examples. All of their books are good but the one on electricity and magnetism was my favorite. I actually learned more from this book than from the textbooks.

I know that some griffiths books dont have solutions to their problems but I dont know if thats true for the electromagnetism book you have. If it is then schaums outline is perfect for you. You said you wanted more detail and example and thats basically schaums outlines are. I used griffiths for quantum mechanics and Ive seen that he is a good author. They have his book on electromagnetism at one of the libraries on my campus so I am going to check it out since you said it was an okay book.

For quantum mechanics I used griffiths but I am going to buy principle of quantum mechanics by shankar. Not only did it get good reviews on amazon. com but I heard from other people that it is good.

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#### MqN

Yeah I agree with you about books. I am constantly looking for good textbooks. For Classical Mechanics, I found this one that I fell in love with, called "Classical Mechanics" by John R Taylor. I think its a new book, its very easy to understand and the author explains everything real good and I think it should appeal to students of different backgrounds. I've used Marion's book before but this one (Taylor's) blows it out of the water. Highly recommended.

As far as electrodynamics, I've used Griffiths and everyone loves that book and I think its ok although I would like to see more details and examples. I am looking for a good EM book so if you know of any then just let me know. I think I am gonna attempt using Griffiths book again and maybe find a solution manual or something.

Any books that you recommend ?
Electricity and Magnetism by Edward Purcell is an excellent book. I think it's better than Griffiths, but not as wealthy in example problems as Griffiths. Very good for beginners or for a better grasp on EM.

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