Calculation of Callan-Symanzik Beta function of QED/QCD to one loop order

In summary, the conversation discusses a project involving the calculation of the Callan-Symanzik beta function of QED and QCD with massless fermions to one loop order. The problem is solved in the textbook by Peskin, but with a lack of rigor, funny assumptions, and some mistakes. The original poster asks for suggestions on other literature that covers the topic in a similar manner to Peskin's approach. One commenter suggests not limiting oneself to just one textbook and resolving any issues with understanding. The original poster later updates that they have found resources to close the gaps in their understanding. Another commenter apologizes for any offense caused and offers to help with any technical details of the calculations.
  • #1
evgkr
6
0
Hi everybody.
I was given a project to calculate Callan-Symanzik beta function of QED and QCD (with massless fermions) to one loop order. This problem is actually solved in Peskin, BUT without the needed rigor, plus with funny assumptions and also a few mistakes.
I have tried for a long time to find where this topic is covered in the manner it is covered in Peskin, but it seems that Peskin's access to the problem although not quite clear to me is pretty original. (Even Callan's original article is not sharing the same access)
My question is: Does anyone knows where I can find literature dealing with Renormalization group from Callan-Symanzik's point og view, and most simillar to Peskin's access to that issue ?

Thanks ahead.
 
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  • #2
Originally posted by evgkr
...project to calculate Callan-Symanzik beta function of QED and QCD (with massless fermions) to one loop order...seems that Peskin's access to the problem although not quite clear to me is pretty original...

I don't have peskin, but they all do it pretty much the same standard way, so there's no need to handcuff yourself to peskin.

Originally posted by evgkr
...problem is actually solved in Peskin, BUT without the needed rigor...

Well, any good textbook is going to require you fill in some of the details since it's by doing calculations that you learn.

Originally posted by evgkr
...plus with funny assumptions and also a few mistakes.

Since peskin has been the standard graduate textbook on the subject for quite a while now. this probably indicates that you don't understand something. I'd start by resolving these issues.
 
  • #3
doesnt Peskin start with the usual Dyson proposed perturbative expansion?
 
  • #4
jeff
I I am quite new in this forum, but I supose that the purpose of this forum is to supply answers to questions and not ctiticizm on ignorance. My question was: Does anybody knows literature with simillar to Peskin's access to C-S equation and NOT whenever I understand or not what is written there or how much calculations I must do to learn. And about your comment on mistakes, I do not know if you are familiar with the fact that EVERY books have mistakes, and also Peskin is full of them, look at the errata in Peskin's site, if you do not believe me.
In the future,please, leave these comments to yourself if you have nothing usefull to prupose.

All
I have managed to close the gaps in this area.
Thanks for help.
 
Last edited:
  • #5
Originally posted by evgkr
jeff
I I am quite new in this forum, but I supose that the purpose of this forum is to supply answers to questions and not ctiticizm on ignorance.

What I posted was based on my own personal experience learning and teaching and was meant to help, not to offend or criticize and I appologize for making you feel attacked. I just didn't want you spending too much time looking for the "ideal" treatment of this subject with all the details spelled out etc because the only place you'll find that is in the notes of some other student who's made the same calculation.

Originally posted by evgkr
And about your comment on mistakes, I do not know if you are familiar with the fact that EVERY books have mistakes, and also Peskin is full of them, look at the errata in Peskin's site, if you do not believe me.

There may be typos remaining in the book, but I'm pretty sure the errata and the book contain no serious logical errors. Can you say something about the parts of peskin that are bothering you? Maybe I can help decipher them. I can also help you with the technical details of these calculations if you want.

Originally posted by evgkr
In the future,please, leave these comments to yourself if you have nothing usefull to prupose.

Just keep in mind that you don't know me and therefore couldn't possibly know for certain how my post was intended. From this standpoint your reaction was presumptious and unjustified and unlike my comments, clearly meant to attack. Likewise, I don't know you, and in the future I'll be more careful with you, but if you habitually fly off the handle like this I definitely won't be wasting any of my time helping you.
 

1. What is the Callan-Symanzik Beta function?

The Callan-Symanzik Beta function is an important mathematical tool in quantum field theory that is used to study the behavior of a physical theory as the energy scale changes. It is a measure of the strength of the interaction between particles and can be used to calculate the running coupling constant, which describes how the strength of the interaction changes at different energy scales.

2. What is QED/QCD?

QED (Quantum Electrodynamics) and QCD (Quantum Chromodynamics) are both quantum field theories that describe the interactions between particles. QED is the theory of the electromagnetic force, while QCD is the theory of the strong nuclear force. Both theories have been extensively tested and are an integral part of the Standard Model of particle physics.

3. What is the importance of calculating the Callan-Symanzik Beta function for QED/QCD?

Calculating the Callan-Symanzik Beta function for QED/QCD is important for understanding the behavior of these theories at different energy scales. By studying the running coupling constant, we can gain insight into the underlying dynamics of these forces and make predictions for experimental results. Additionally, the Callan-Symanzik Beta function is an essential tool for studying the renormalization of these theories, which is necessary for making meaningful calculations.

4. What is the one-loop order in the calculation of the Callan-Symanzik Beta function?

The one-loop order refers to the first order of perturbation theory in the calculation of the Callan-Symanzik Beta function. This means that only the simplest diagrams, involving one loop of particles, are taken into account in the calculation. Higher orders of perturbation theory involve more complex diagrams and can lead to more accurate results, but are significantly more difficult to calculate.

5. What is the significance of the one-loop order in the calculation of the Callan-Symanzik Beta function?

The one-loop order is significant because it provides the leading contribution to the calculation of the Callan-Symanzik Beta function. It is often the first step in calculating higher order corrections and can give valuable insight into the behavior of the theory. Additionally, the one-loop order is usually the most feasible to calculate, making it a practical starting point for studying the Callan-Symanzik Beta function.

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