Basic question about Feynman Diagrams

In summary, vertices in Feynman diagrams can have more than three particles going in or out from them, depending on the number of fields multiplied together in the interaction term of the Lagrangian. While most Feynman vertices have three arms attached, gluons can make a 4-vertex and interactions in electroweak theory can lead to both 3- and 4-particle vertices. In QED and Weak Force processes, the vertices are typically 3-vertices, but this can vary depending on the specific interaction terms in the Lagrangian.
  • #1
McLaren Rulez
292
3
Can a vertex of a Feynman diagram have more than three particles going in or out from it? Assuming all other conservation laws are obeyed, of course. I haven't seen this being explicitly stated but all the Feynman vertices I have seen have three arms attached. Thank you.
 
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  • #2
You can indeed. For instance gluons can make a 4 vertex.
 
  • #3
An interaction term in the Lagrangian which is trilinear leads to a 3-particle vertex, while one which is quadrilinear leads to a 4-particle vertex. These things occur for example in electroweak theory. The kinetic energy term for the W boson is 1/4 WμνWμν where Wμν = ∂μWν - ∂νWμ - gWμ x Wν, which leads among other things to a 4-particle WWWW vertex. Also there is a WWhh vertex from its interaction with the Higgs.
 
  • #4
Thank you for the quick replies. I do not know about the interaction terms in the Lagrangian. I am just learning to draw Feynman Diagrams for basic QED and Weak Force processes. So, in these cases, are my vertices 3 vertices or 4 vertices or are both okay? Thank you.
 
  • #5
McLaren Rulez said:
Thank you for the quick replies. I do not know about the interaction terms in the Lagrangian. I am just learning to draw Feynman Diagrams for basic QED and Weak Force processes. So, in these cases, are my vertices 3 vertices or 4 vertices or are both okay? Thank you.
In QED, the interaction term from the Lagrangian is [itex]e\bar{\psi}\gamma^\mu A_\mu \psi[/itex]. Since three fields take part in the interaction, these are 3-vertices.
 
  • #6
McLaren Rulez said:
I do not know about the interaction terms in the Lagrangian. I am just learning to draw Feynman Diagrams

But that's what Feynman diagrams are.

They are not little cartoons describing collisions between billiard-ball like particles. They are a calculational shorthand for terms in a Lagrangian.
 
  • #7
The simpler electroweak processes are all three-vertices:
  • two fermions interacting with a W boson;
  • two fermions interacting with a Z boson; or
  • two fermions or a W boson interacting with a photon.
In general, the number of fields multiplied together in each Lagrangian term imply interactions with that number of particpants. If there are only two - in which case they will always be a field and conjugate of either the same field or its chiral partner, the term represents
  • a kinetic term, if it has one or more partial differential operators (eg [itex]\bar{\psi}\gamma^{\mu}\partial_{\mu}\psi[/itex] or [itex]F^{\mu\nu}F_{\mu\nu}[/itex]), or
  • a mass term, if not (eg [itex]m\bar{\psi}_L\psi_R[/itex]).
([itex]F^{\mu\nu}F_{\mu\nu}[/itex] does have differential operators but they are "hidden" in its definition ([itex]F^{\mu\nu} = \partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}[/itex])).
 
  • #8
Thank you! I think I have a clearer picture in my head now.
 

What are Feynman diagrams and how are they used in physics?

Feynman diagrams are graphical representations of particle interactions in quantum field theory. They are used to calculate the probability of a particular particle interaction occurring.

How do I read a Feynman diagram?

A Feynman diagram consists of lines and vertices. The lines represent particles and the vertices represent interactions between particles. Time flows from left to right, and particles are represented by arrows pointing in the direction of their motion.

What is the significance of the direction of the arrows in a Feynman diagram?

The direction of the arrows in a Feynman diagram represents the flow of time. In particle interactions, time always moves forward, so the arrows in a Feynman diagram should always point from left to right.

Do all particle interactions have a corresponding Feynman diagram?

No, not all particle interactions have a corresponding Feynman diagram. Feynman diagrams are only used to represent interactions that occur at the quantum level, and some interactions may occur at a larger scale that can be described using other mathematical models.

How accurate are Feynman diagrams in predicting particle interactions?

Feynman diagrams are highly accurate in predicting particle interactions. They have been extensively tested and have been shown to accurately predict the outcomes of many experiments in particle physics. However, they are not a complete theory and may not always accurately predict interactions in extreme conditions such as at very high energies.

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