Calculating Symmetry Factors for Graphs: Reasoning Behind Findings

  • Thread starter kau
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In summary, the conversation is about calculating the symmetry factors for two graphs using the field contraction method. The speaker is getting incorrect results, but has found a logical explanation for this. They discuss permutations and overcounting in Feynman diagrams, leading to a symmetry factor of 2 for the first diagram and 4 for the second.
  • #1
kau
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consider the following two graphs. I want to calculate the symmetry factors for them . I am using field contraction method for that. but I am getting 2 for the 2 vertex diagram and 1 for the zero vertex diagram where it should be 4 and two respectively. Can anyone do it for me. I am writing briefly the reason behind my findings. i am considering $$\phi^3$$ theory. So for vertex zero case i don't have any factors left. In case of two vertex case. say I am denoting two vertices as v and w and the sources as x and y. ok. now x can be combined with 6 possible ways and therefore y can be combined with 2 possible ways. now if i call that one v. then i am left with one field in v and 3 in w. they can combine 3 ways. so i got 6*3*2. now i have to divide it by 2*(3!*3!). and this would give me 1/2. so the symmetry factor is two. but that is a wrong answer. so where did i missed the point.??
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
Greg Bernhardt said:
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #4
i have found some logical explanation behind these things. actually what happen in case of drawing a feynman diagram is that if every term is properly normalized then all the factors get canceled appropriately. in that case we consider that permutations of propagators,vertices,externals lead to different diagram. but it turns out that some of these permutations are same. so we have over counted them,therefore we ave to divide the amplitude(we get following feynman rules) by that factor. like in the first diagram we can exchange the two sources and it is same as reversing the propagator,but we have considered both. so s=2. and in the second case you can exchange the derivatives at the vertex (connected to sources) and that is same as exchangin the propagators along with sources. so this gives 2. another two comes due to the identical figures due to exchange of two legs of the curved propagator. this gives another two. so we have total 4 as a symmetry factor.
 

1. What is the purpose of calculating symmetry factors for graphs?

The purpose of calculating symmetry factors for graphs is to identify patterns and relationships between different parts of a graph. This can help in understanding the structure and behavior of the graph, as well as making predictions about its properties.

2. How do you calculate symmetry factors for graphs?

To calculate symmetry factors for graphs, you first need to identify all the possible symmetries of the graph, such as rotations, reflections, and translations. Then, you use these symmetries to group together equivalent parts of the graph and count the number of distinct groups. The number of groups is the symmetry factor for that graph.

3. What is the significance of symmetry factors in graph theory?

Symmetry factors play a significant role in graph theory as they provide insight into the structure and properties of a graph. They can help in identifying symmetries, automorphisms, and other important characteristics of a graph. They also have applications in various fields, such as chemistry, physics, and computer science.

4. How do the findings from calculating symmetry factors contribute to understanding a graph?

The findings from calculating symmetry factors provide valuable information about the symmetries and structure of a graph. This can help in understanding the relationships between different parts of the graph and identifying any patterns or regularities. It can also aid in predicting the behavior of the graph and identifying any special properties it may have.

5. Can symmetry factors be calculated for any type of graph?

Yes, symmetry factors can be calculated for any type of graph, including directed and undirected graphs, weighted graphs, and even infinite graphs. However, the method for calculating symmetry factors may vary depending on the type of graph. In some cases, it may not be possible to calculate symmetry factors if the graph does not have any symmetries.

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