How to calculate symmetry factor of Feynman graphs?

• kau
In summary, the first diagram has symmetry factor =2 because you can swap all three sources. The third diagram has symmetry factor =1 because you can only swap the lower two parts of the big bubble which is holding the lower loop.
kau
I am reading Srednicki's book and I am stuck at this point of calculating symmetry factors for Feynman's Graph in the context of dealing with interacting scalar field. First of all my question is what is the standard procedure to calculate it. The way Srednicki has talked about it is that if interchanging any two things match with any other swapping then we should take into account factor 2 for each of that case. First of all I didn't understand what does it mean to interchange two legs of vertices. which part is called leg of a vertex? alright then consider the four diagrams I have attached below. And explain me the factors in each case using the kind of arguments like swapping this and that and so on. then answer these ques.. In the first diagram can I swap all three sources?? in the third diagram can I swap the lower two parts of the big bubble which is holding the lower loop?? Please help me. thanks.

For example the:
https://www.physicsforums.com/attachments/e-4-jpg.73744/
has symmetry factor =2
One way to determine symmetry factors is by using the Wick's theorem and field contractions. The rules then come out naturally after you get used in using that correctly...
You can understan it's 2 because 2 diagrams give exactly the same interaction term...
if you name the vertices A and B in that picture, whether you bring the two left external legs to A and the right to B, or bring the left to B and the right to A you get the same term...

I don't know the way of path integrals... but you can search for "vertices derivatives and symmetry factors" and find some results that can help you personally.

Last edited:
kau said:
I am reading Srednicki's book and I am stuck at this point of calculating symmetry factors for Feynman's Graph in the context of dealing with interacting scalar field. First of all my question is what is the standard procedure to calculate it. The way Srednicki has talked about it is that if interchanging any two things match with any other swapping then we should take into account factor 2 for each of that case. First of all I didn't understand what does it mean to interchange two legs of vertices. which part is called leg of a vertex? alright then consider the four diagrams I have attached below. And explain me the factors in each case using the kind of arguments like swapping this and that and so on. then answer these ques.. In the first diagram can I swap all three sources?? in the third diagram can I swap the lower two parts of the big bubble which is holding the lower loop?? Please help me. thanks.
This is extreamly tedious business to explain in here. See the pdf below. If this does not help you, then you should ask your instructor to explain it to you. One really needs 2-3 blackboards for that :)

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1. What is the definition of symmetry factor in Feynman graphs?

The symmetry factor of a Feynman graph is a mathematical factor that takes into account the number of ways in which the graph can be redrawn without changing the underlying physics. It is used to correct for overcounting in perturbative calculations.

2. How is symmetry factor calculated for a Feynman graph?

The symmetry factor is calculated by counting the number of ways in which the graph can be redrawn by interchanging identical particles or external lines, and dividing this number by the total number of identical particles or external lines. This gives the probability of obtaining the same graph through different permutations.

3. Why is it important to calculate the symmetry factor in Feynman graphs?

The symmetry factor is important because it allows for more accurate calculations in perturbative quantum field theory. By correcting for overcounting, it ensures that the calculated probability amplitudes are in agreement with experimental results.

4. Can the symmetry factor be negative?

No, the symmetry factor of a Feynman graph cannot be negative. It is always a positive number, as it represents the probability of obtaining the same graph through different permutations.

5. Are there any shortcuts or tricks for calculating symmetry factors in Feynman graphs?

There are some shortcuts that can be used to calculate symmetry factors in certain cases, such as when there are only a few identical particles or external lines in the graph. However, in general, the symmetry factor must be calculated by counting all possible permutations.

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