Understanding Feynman Diagrams: A Beginner's Guide

[ice109]

Homework Statement

i've never had a QM class let alone QFT, I've only even had intro physics 1 & 2, but I've been given a problem that is very similar to this:

$$-ie^3 \int {d^4 q \over (2\pi)^4} \gamma^\mu {i (\gamma^\alpha (r-q)_\alpha + m) \over (r-q)^2 - m^2 + i \epsilon} \gamma^\rho {i (\gamma^\beta (p-q)_\beta + m) \over (p-q)^2 - m^2 + i \epsilon} \gamma^\nu {-i g_{\mu\nu} \over q^2 + i\epsilon }$$

it's obviously not essential i know how to do this for a test or anything, but what can i read to be able to begin to attack this problem? I've the sections from peskin and shroeder on feyman parameters and dimensional regularization but i can't really make sense of those either.

any ideas? I'm going to be talking to one of my professors about it on monday hopefully.

 

[Timo]

<I hit the wrong button; wanted to press preview>

 

[olgranpappy]

Homework Statement

i've never had a QM class let alone QFT, I've only even had intro physics 1 & 2, but I've been given a problem that is very similar to this:

$$-ie^3 \int {d^4 q \over (2\pi)^4} \gamma^\mu {i (\gamma^\alpha (r-q)_\alpha + m) \over (r-q)^2 - m^2 + i \epsilon} \gamma^\rho {i (\gamma^\beta (p-q)_\beta + m) \over (p-q)^2 - m^2 + i \epsilon} \gamma^\nu {-i g_{\mu\nu} \over q^2 + i\epsilon }$$

it's obviously not essential i know how to do this for a test or anything, but what can i read to be able to begin to attack this problem? I've the sections from peskin and shroeder on feyman parameters and dimensional regularization but i can't really make sense of those either.

any ideas? I'm going to be talking to one of my professors about it on monday hopefully.

Looks like you are calculating a radiative correction to the QED vertex.

I think Peskin and Schroeder go over that. If not, it is a well-known problem that you should be able to find in textbooks.

 

[ice109]

Looks like you are calculating a radiative correction to the QED vertex.

I think Peskin and Schroeder go over that. If not, it is a well-known problem that you should be able to find in textbooks.

later i'll post the problem I'm doing, but like i said that is not the problem I'm doing. also i don't need to know how to mechanically do it, it's already done, i would like to be able to understand how to do it

 

[Dick]

That's a titanic question, along the lines of 'how I do all thermodynamics problems?'. You know that, right? This is a homework helpers forum, not a lecture series. You'll have to be much more specific.

 

[ice109]

That's a titanic question, along the lines of 'how I do all thermodynamics problems?'. You know that, right? This is a homework helpers forum, not a lecture series. You'll have to be much more specific.

well you could start by defining all the symbols for me

 

[PhysiSmo]

check out "Quantum Field Theory" by L. Ryder. He explains everything you need in section 9.5.

 

[mjsd]

Homework Statement

i've never had a QM class let alone QFT, I've only even had intro physics 1 & 2, but I've been given a problem that is very similar to this:

$$-ie^3 \int {d^4 q \over (2\pi)^4} \gamma^\mu {i (\gamma^\alpha (r-q)_\alpha + m) \over (r-q)^2 - m^2 + i \epsilon} \gamma^\rho {i (\gamma^\beta (p-q)_\beta + m) \over (p-q)^2 - m^2 + i \epsilon} \gamma^\nu {-i g_{\mu\nu} \over q^2 + i\epsilon }$$

understanding the symbols eh?

$$\gamma^\mu$$ these are gamma matrices from Dirac equation the same greek superscripts or subscripts needed to be sum over.

$$+i\epsilon$$ is supposedly infinitestimal. it is included in the propagator to avoid the poles when integrating.

$$q, r-q, p-q$$ etc. are momenta. $$m$$ is mass of the particle

$$g^{\mu\nu}$$ is the metric tensor: diag(1,-1,-1,-1) in some convention.

 

[nrqed]

Homework Statement

i've never had a QM class let alone QFT, I've only even had intro physics 1 & 2, but I've been given a problem that is very similar to this:

$$-ie^3 \int {d^4 q \over (2\pi)^4} \gamma^\mu {i (\gamma^\alpha (r-q)_\alpha + m) \over (r-q)^2 - m^2 + i \epsilon} \gamma^\rho {i (\gamma^\beta (p-q)_\beta + m) \over (p-q)^2 - m^2 + i \epsilon} \gamma^\nu {-i g_{\mu\nu} \over q^2 + i\epsilon }$$

it's obviously not essential i know how to do this for a test or anything, but what can i read to be able to begin to attack this problem? I've the sections from peskin and shroeder on feyman parameters and dimensional regularization but i can't really make sense of those either.

any ideas? I'm going to be talking to one of my professors about it on monday hopefully.

What is the goal of doing this calculation if you haven't even had a QM class?

If you haven't learned a bit of QFT, the only thing people can do here is to show you how to mechanically do it. But later in the thread, you say that you have already done that and you want to understand what you are doing. But there is no way you can really understand what this is about without a lot of QM and a fair amount of QFT. We would have to cover the equivalent of 4-5 advanced classes before really explaining this calculation.

But it's not clear at what level you want to understand this expression. You would have to be more specific.
Do you know the Feynman diagram associated to this integral? Do you know
what each term corresponds to in the diagram?