U-Channel Diagrams in QFT: A Closer Look

In summary, the interaction vertices in the nucleon-antinucleon case do not allow for a u-channel diagram due to the violation of nucleon number conservation and the distinguishability of the states. This is different from the nucleon-nucleon case where both t and u-channel diagrams are possible due to the indistinguishability of the nucleons.
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  • #2
The interaction vertices don't allow for a u-channel diagram where the final state nucleon and antinucleon cross. You can check this by trying to draw such a diagram by starting with the initial and final state lines and then trying to insert vertices to connect them. If you consider the nucleon-nucleon interaction, you would find t and u-channel diagrams, but no s-channel.
 
  • #3
fzero said:
The interaction vertices don't allow for a u-channel diagram where the final state nucleon and antinucleon cross. You can check this by trying to draw such a diagram by starting with the initial and final state lines and then trying to insert vertices to connect them. If you consider the nucleon-nucleon interaction, you would find t and u-channel diagrams, but no s-channel.

I think I see why there is no s channel in the nucleon nucleon case. Is this because, if there were an s channel diagram, we would have 2 [itex]\psi[/itex] particles on the left of the 1st vertex and 0 [itex]\psi[/itex] particles on the right? Since the number of psi particles is a quantum number, it must be conserved and so this diagram is unphysical.

I tried applying a similar argument to the u channel diagram in the nucleon-antinucleon case but I just cannot see why it won't work! Can you elaborate please?
 
  • #4
latentcorpse said:
I think I see why there is no s channel in the nucleon nucleon case. Is this because, if there were an s channel diagram, we would have 2 [itex]\psi[/itex] particles on the left of the 1st vertex and 0 [itex]\psi[/itex] particles on the right? Since the number of psi particles is a quantum number, it must be conserved and so this diagram is unphysical.

Yes the interaction vertex conserves the nucleon number.

I tried applying a similar argument to the u channel diagram in the nucleon-antinucleon case but I just cannot see why it won't work! Can you elaborate please?

To form a u-channel diagram, you would need to have a vertex that turned a nucleon into an antinucleon, but this violates nucleon number.

We can also note that for the n-n interaction in Fig 9, the u-channel is just a permutation of the final state momenta when compared to the t-channel. This is possible because the nucleons are indistinguishable. In the nucleon-antinucleon case, we can't just swap the momenta because the states are distinguishable.
 
  • #5


U-channel diagrams are a type of Feynman diagram used in quantum field theory (QFT) to represent interactions between particles. In Figure 13 on page 64 of the provided notes, the author discusses the possibility of a u-channel diagram, which would involve particles interacting in a different way than the diagrams shown in the figure. However, the author concludes that this type of diagram is not possible in the given scenario.

There are a few reasons why a u-channel diagram may not be possible in this case. First, it may violate certain conservation laws, such as energy or momentum conservation. These laws are fundamental principles in physics and must be obeyed in any physical process.

Additionally, the interaction between the particles in the given scenario may not allow for a u-channel diagram. In QFT, particles interact through the exchange of virtual particles, and the type of interaction determines which types of virtual particles can be exchanged. If the interaction does not allow for the exchange of the necessary virtual particles, then a u-channel diagram would not be possible.

Furthermore, the author notes that the particles involved in the interaction must have different charges for a u-channel diagram to be possible. If the particles have the same charge, then the diagram would not be able to represent the interaction.

In summary, the absence of a u-channel diagram in Figure 13 on page 64 can be attributed to violations of conservation laws, the nature of the interaction between particles, and the charges of the particles involved. These factors must be taken into account when considering the possibility of different types of Feynman diagrams in QFT.
 

1. What is a U-Channel Diagram in QFT?

A U-Channel diagram is a type of Feynman diagram used in quantum field theory (QFT) to visualize and calculate the interactions between elementary particles.

2. How is a U-Channel Diagram different from other Feynman diagrams?

A U-Channel diagram represents the exchange of a particle between two interacting particles, while other Feynman diagrams typically represent the direct interaction between particles.

3. What is the significance of U-Channel diagrams in QFT?

U-Channel diagrams play a crucial role in QFT as they help in calculating the probability of particle interactions and predicting the outcomes of experiments.

4. Can U-Channel diagrams be used for all particle interactions?

No, U-Channel diagrams are specifically used for particles that interact through the exchange of a third particle, such as the weak nuclear force.

5. Are U-Channel diagrams based on experimental evidence?

Yes, U-Channel diagrams are based on experimental evidence and have been successfully used to predict and explain the outcomes of many experiments in the field of particle physics.

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