New Feynman Rules in QED from Counterterms

In summary, the conversation discusses the topic of renormalization in QED, with a focus on two main issues: the representation of counter-terms in Feynman diagrams and the purpose of renormalization conditions. The circles with crosses in the Feynman diagrams represent the counter-terms themselves, and the renormalization conditions are necessary to determine the values of these counter-terms. Overall, the conversation provides a better understanding of the complex concept of renormalization in QED.
  • #1
blackie1008
5
0
Hi,

I have been looking at the renormalisation of QED and been using Peskin & Schroeder. I understand (I think) what is going on, but I am slightly confused over 2 issues:

1. In the new feynman rules from the counterterms, the feynman diagrams all have a small circle with a cross in them...what do these represent? (P&S p332, fig 10.4)

2. why do we need the renormalization conditions? (P&S p331-331 eq 10.40)

Help would be much appreciated!

Thanks
 
Physics news on Phys.org
  • #2
For question 1., the circles represent the counter-terms themselves.

For question 2., the renormalization conditions are required to fix the counterterms. For example the bare mass in the Lagrangian is [tex]m_{0}[/tex]. We split this into the physical mass and the counterterm, [tex]m_{0} = m + \delta m[/tex]. However you need the figure out what [tex]\delta m[/tex] should be so that the physical mass is [tex]m[/tex]. The physical mass being [tex]m[/tex] means that [tex]\Sigma(m^{2}) = 0[/tex]. This provides you with the equation you need to obtain [tex]\delta m[/tex].
 
  • #3
Thanks for clearing up question 2, but as for question 1, by "representing the counterterms themselves" do you mean that it represents all the contributions that are taken into account?
 
  • #4
blackie1008 said:
Thanks for clearing up question 2, but as for question 1, by "representing the counterterms themselves" do you mean that it represents all the contributions that are taken into account?
The black circle with for the interaction vertex represents [tex]\delta \lambda[/tex] to all orders. At a given order of perturbation theory it can only stand for [tex]\delta \lambda[/tex] to that order or less. For instance let's say you were computing at third order, you could have a diagram with one normal interaction vertex and one counter-term interaction vertex, the counter-term vertex will contain the counter-term to second order, so you will get [tex]\lambda[/tex] from the usual vertex and [tex]\lambda^{2}[/tex] from the counter-term vertex, giving you a third order contribution.
 
  • #5
Ahhh ok think I have got it now!

Thanks for the help, its much appreciated!
 

1. What are the "New Feynman Rules" in QED from Counterterms?

The "New Feynman Rules" in QED from Counterterms refer to a set of mathematical rules developed by Richard Feynman in quantum electrodynamics (QED) to describe the interactions between electrons and photons. These rules take into account counterterms, which are corrections to the original Feynman rules that are necessary to account for divergences in the calculations.

2. How are the "New Feynman Rules" different from the original Feynman rules in QED?

The "New Feynman Rules" in QED from Counterterms differ from the original Feynman rules in that they include additional terms to account for counterterms. These counterterms are necessary to ensure that the calculations are mathematically consistent and do not produce infinite or nonsensical results.

3. Why were the "New Feynman Rules" developed in QED?

The "New Feynman Rules" were developed in QED to address the issue of divergences in the original Feynman rules. These divergences arise due to the infinite self-energy of the electron and the infinite energy of the vacuum. The inclusion of counterterms in the "New Feynman Rules" allows for these divergences to be cancelled out and for more accurate calculations to be made.

4. How are the "New Feynman Rules" applied in QED calculations?

The "New Feynman Rules" in QED from Counterterms are applied in calculations by adding the counterterms to the original Feynman rules. This results in more complex mathematical expressions, but ultimately leads to more accurate and reliable results. These rules are used extensively in theoretical calculations in the field of particle physics.

5. What impact do the "New Feynman Rules" have in the field of particle physics?

The "New Feynman Rules" in QED from Counterterms have had a significant impact in the field of particle physics. They have allowed for more accurate and precise calculations to be made, leading to a better understanding of the interactions between particles. They have also been applied to other quantum field theories, serving as a foundation for further advancements in the field.

Similar threads

  • Quantum Physics
Replies
6
Views
817
  • Quantum Physics
Replies
6
Views
2K
  • Quantum Physics
Replies
3
Views
1K
  • Quantum Physics
Replies
1
Views
1K
  • Quantum Physics
Replies
6
Views
958
  • High Energy, Nuclear, Particle Physics
Replies
5
Views
944
  • Quantum Physics
Replies
23
Views
6K
Replies
6
Views
1K
Replies
4
Views
2K
  • Quantum Physics
Replies
10
Views
2K
Back
Top