QFT phi3 Feynman diagrams and correlation function

In summary, the conversation discusses the process of drawing connected graphs up to one-loop approximation for a scalar theory with an interaction part of \frac{g}{3!} \phi^3. The relevant correlation function is shown to be the product of external leg propagators and the amputated Green's function up to order g^2. The inclusion of self-interacting graphs is debated, with the conclusion that they should not be included in the first place as they do not contribute to the T-Matrix. The definition of "connected" graphs is also discussed, with the understanding that they are those with all external lines connected to each other.
  • #1
ChrisVer
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I have some difficulty understanding how to go about with this problem:
For a scalar theory whose interaction part is [itex] \frac{g}{3!} \phi^3[/itex], draw all connected graphs up to one-loop approximation contributing to the process [itex]\phi (k_1) \phi (k_2) \rightarrow \phi (k_3) \phi (k_4)[/itex].
I came up with several graphs, you can see them in the attached picture (they are up to ~g^4 order). I am not sure about the self-interaction diagrams, but I think they are considered in the connected graphs (they are not away from the external legs).

To order [itex]g^2[/itex] show that the relevant correlation function is the product of the external leg propagators times the amputated Green's function. What are the graphs of the amputated correlation function ?
I am not sure whether here I'll have to also include the g^2 self-interacting graphs... without them I seem to be getting:
[itex]G \sim g^2 \Big( \frac{1}{s+m^2} + \frac{1}{t + m^2} + \frac{1}{u+m^2}\Big) \delta^4 ( k_1 + k_2 - k_3 - k_4)[/itex]
which looks OK compared to also including them.
 

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  • #2
By "self-interacting" you mean e.g. the first two in the second row? You are supposed to only consider connected graphs, so these two (and the very first one, and also some later ones) should not be there in the first place.

Also, I think there are more diagrams at 1-loop, e.g. more self energies and tadpoles...
 
  • #3
Dr.AbeNikIanEdL said:
You are supposed to only consider connected graphs, so these two (and the very first one, and also some later ones) should not be there in the first place

I thought connected graphs were those that didn't have loops away from the internal/external legs (contributing to vacuum, which cancels out).

Dr.AbeNikIanEdL said:
Also, I think there are more diagrams at 1-loop, e.g. more self energies and tadpoles...
hmm, maybe
 
  • #4
ChrisVer said:
I thought connected graphs were those that didn't have loops away from the internal/external legs (contributing to vacuum, which cancels out).

At least in the conventions I am aware of, "connected" means that all external lines are connected to each other. A better definition might be something like "momentum conservation is not fulfilled by a subset of external momenta". These are the ones that actually give a contribution to the T-Matrix.
 

FAQ: QFT phi3 Feynman diagrams and correlation function

1. What is QFT phi3 and how is it related to Feynman diagrams?

QFT phi3, or Quantum Field Theory with a scalar field, is a theoretical framework used to describe the behavior of particles at a subatomic level. Feynman diagrams are visual representations of mathematical calculations used in QFT to predict the probability of particle interactions.

2. How are correlation functions used in QFT phi3?

Correlation functions are used in QFT phi3 to calculate the probability of a certain particle interaction occurring at a specific time and location. They are also used to study the behavior of quantum fields and their interactions.

3. What is the significance of Feynman diagrams in QFT phi3?

Feynman diagrams are a crucial tool in QFT phi3 as they allow for the visualization of complex mathematical calculations and aid in the prediction of particle interactions. They also help to simplify the calculations and make them more manageable.

4. How do Feynman diagrams and correlation functions relate to the concept of renormalization in QFT?

Renormalization is a technique used in QFT to remove infinities from calculations and make them more accurate. Feynman diagrams and correlation functions are used in this process to calculate the necessary corrections and adjust the parameters of a theory.

5. Can QFT phi3 Feynman diagrams and correlation functions be used to make predictions about real-world phenomena?

Yes, QFT phi3 Feynman diagrams and correlation functions have been successfully applied in various fields, including particle physics, condensed matter physics, and cosmology. They have led to the discovery of new particles and have been used to make accurate predictions about the behavior of matter and energy at a subatomic level.

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