Is the Correct Delta Function for a QED Vertex \(\delta(p+q-k)\)?

In summary, momentum flow in QED vertex refers to the transfer of momentum between particles at the vertex in Quantum Electrodynamics. It is calculated using Feynman diagrams and is crucial in understanding particle interactions and fundamental forces at the quantum level. The momentum flow determines the strength and direction of particle interactions and can be observed experimentally through high-energy particle physics experiments.
  • #1
kilokhan
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say I have a QED vertex with an anti-fermion (p) going in and a fermion (q) and photon(k) coming out. Since the momentum flow is supposed to be along the direction of particle number flow, wouldn't this mean that the delta function at that vertex would be [tex]\delta(-p-q-k)[/tex] ? that doesn't seem to make sense. What is the correct delta function, and how do I get it?
 
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  • #2
You can't have a fermion coming in and an antifermion coming out; that violates charge conservation ...
 
  • #3


The momentum flow in a QED vertex is indeed along the direction of particle number flow. However, the delta function at the vertex should be \delta(p+q-k), rather than \delta(-p-q-k). This is because the momentum of the anti-fermion (p) is flowing in the opposite direction of the fermion (q) and photon (k), so the total momentum at the vertex should be conserved and equal to the sum of the individual momenta. Therefore, the correct delta function should take into account the direction of momentum flow, which is why it is \delta(p+q-k).

To obtain this delta function, you can use the conservation laws of energy and momentum in QED. By setting the total energy and momentum of the incoming and outgoing particles to be equal, you can derive the correct delta function at the vertex. Additionally, you can also use Feynman diagrams and Feynman rules to calculate the amplitude of the process, which will also give you the correct delta function.

It is important to note that the delta function at the vertex is not a physical quantity, but rather a mathematical tool used in calculations. It helps to simplify the calculations and ensure that energy and momentum are conserved at every vertex in the Feynman diagram.

In summary, the correct delta function for a QED vertex with an anti-fermion (p) going in and a fermion (q) and photon (k) coming out is \delta(p+q-k). This can be obtained through the conservation laws of energy and momentum or by using Feynman diagrams and rules.
 

Related to Is the Correct Delta Function for a QED Vertex \(\delta(p+q-k)\)?

1. What is momentum flow in QED vertex?

Momentum flow in QED vertex refers to the transfer of momentum between particles at the vertex, or point of interaction, in Quantum Electrodynamics (QED). This is important in understanding the behavior and interactions of fundamental particles, such as electrons and photons, in the quantum world.

2. How is momentum flow calculated in QED vertex?

Momentum flow in QED vertex is calculated using Feynman diagrams, which represent the different possible interactions between particles. These diagrams use mathematical equations and rules to determine the momentum flow at each vertex and track the movement of particles through space and time.

3. What is the significance of momentum flow in QED vertex?

The momentum flow at QED vertices is crucial in understanding the fundamental forces and interactions between particles at the quantum level. It allows for the prediction and explanation of the behavior of particles, such as the scattering of electrons and photons, and the creation and annihilation of particles and antiparticles.

4. How does momentum flow affect particle interactions in QED vertex?

The momentum flow at QED vertices determines the strength and direction of particle interactions. This is because momentum must be conserved at each vertex, meaning that the total momentum before and after the interaction must be equal. Therefore, the momentum flow plays a crucial role in determining the outcome of particle interactions in QED.

5. Can momentum flow in QED vertex be observed experimentally?

Yes, momentum flow in QED vertex can be observed experimentally through high-energy particle physics experiments. By analyzing the trajectories and energies of particles before and after their interactions at the vertex, scientists can indirectly measure the momentum flow and validate the predictions of QED.

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