Can One Interaction Term Represent Multiple Vertices in Feynman Diagrams?

In summary, the interaction term in the Lagrangian represents the vertices in Feynman diagrams. In the given example, the Lagrangian L = eψγμψAμ can represent both the vertices shown and there is no need for two separate terms. The Lagrangian provides the rules for constructing diagrams, with the vertices corresponding to coupling constants and conservation laws. Higher order diagrams can also be constructed using the same vertices.
  • #1
Josh1079
47
0
Hi,

My question is that can one interaction term represent two vertices?

For instance, can the lagrangian interaction terms L = eψγμψAμ represent a feynman diagram like these:
eetoee1.png


or should there be two terms in the lagrangian to construct such diagrams?

Thanks!
 
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  • #2
The interaction term gives you the vertices. The vertices in your two diagrams are both the same.
 
  • #3
Thanks for the reply!

So I guess I can draw the same vertices several times in a diagram with the interaction term appearing only once in the Lagrangian?
 
  • #4
Yes, those correspond to higher orders in perturbation theory.
 
  • #5
Got it!

Thank you so much Orodruin!
 
  • #6
the lagrangian gives you the rules by which you can draw diagrams... afterall the vertices in a diagram only correspond to a coupling constant and conservation of energy/momentum.
 

1. What is an interaction term in statistical analysis?

An interaction term is a variable created by multiplying two or more independent variables together in a regression model. It is used to account for the combined effect of the independent variables on the dependent variable. For example, in a study on the effect of education level and income level on job satisfaction, an interaction term would be created by multiplying the two variables together to see if the combined effect is different from the sum of their individual effects.

2. How do you interpret an interaction term in a regression model?

The interpretation of an interaction term depends on the type of regression model being used. In a linear regression model, the coefficient of the interaction term represents the change in the slope of the relationship between the independent variables and the dependent variable. In logistic regression, the coefficient of the interaction term represents the change in the log odds of the outcome. It is important to also consider the p-value of the interaction term to determine if it is statistically significant.

3. What is a vertex in a graph?

A vertex, also known as a node, is a point on a graph where two or more lines intersect. In a graph, vertices represent individual data points or the starting and ending points of a line. They are often represented by a dot or circle and are labeled with a letter or number for identification purposes.

4. How do you determine the degree of a vertex in a graph?

The degree of a vertex is the number of edges, or lines, connected to that vertex. In a directed graph, the degree is divided into the in-degree, which is the number of edges coming into the vertex, and the out-degree, which is the number of edges going out from the vertex. In an undirected graph, the degree is the same for both incoming and outgoing edges.

5. Why are vertices important in network analysis?

Vertices are important in network analysis because they represent the entities or individuals in a network and their connections to other entities. By analyzing the relationships between vertices, we can better understand the structure and dynamics of a network. Vertices also allow us to analyze the centrality of nodes, identify key players, and detect patterns in the network.

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