How does one find the Feynman diagrams?

In summary, the conversation discusses the process of representing Feynman diagrams in Quantum Field Theory and how to find them up to a specific order for a particular interaction lagrangian. It is explained that the expansion of the n-point function can be difficult and Wick's theorem can be challenging to use, so Feynman rules are developed to simplify the process. To find diagrams up to a certain order, one must make a list of all couplings and then find diagrams that only include those couplings with the correct number of external legs. While this can be done manually for low orders, there are also tools available to automate the process.
  • #1
leo.
96
5
I'm studying Quantum Field Theory and the main books I'm reading (Peskin and Schwartz) present Feynman diagrams something like this: one first derive how to express with perturbation theory the [itex]n[/itex]-point correlation functions, and then represent each term by a diagram. It is then derived the Feynman rules that allows one to do the backwards process: given a diagram, find out the terms in the expansion.

The point that all books make, at least in my opinion, is: computing the expansion is hard and using Wick's theorem is quite hard, so one develops these Feynman rules so that the process becomes: (1st) find the Feynman diagrams and (2nd) associate the number to the diagrams according to the rules.

My whole question is: considering a particular interaction lagrangian, how does one finds the Feynman diagrams up to some specific order?

It obviously isn't by expanding the [itex]n[/itex]-point function, because if it was there would be no point in drawing the diagrams anyway, since the expansion would already be known.

The only thing I can figure out is that in the expansion of the [itex]n[/itex]-point each diagram has [itex]n[/itex] external points and expansion to order [itex]\lambda^k[/itex] will have [itex]k[/itex] internal points.

So considering for example the [itex]\mathcal{L}_{\mathrm{int}} = \lambda \phi^4/4![/itex] theory, how can I find the Feynman diagrams up to order [itex]\lambda^2[/itex]?
 
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  • #2
Make a list of all couplings.
Then find all diagrams up to a given order that only include these couplings and have the right external legs.

While you can do this manually for low orders, there are tools that can do this automatically. Just try everything and discard what doesn't work.
 

FAQ: How does one find the Feynman diagrams?

1. How are Feynman diagrams used in physics?

Feynman diagrams are graphical representations of mathematical equations that are used to describe and visualize interactions between subatomic particles in quantum field theory. They are commonly used in particle physics to understand the behavior of particles and their interactions.

2. Who invented the Feynman diagrams?

The Feynman diagrams were invented by American physicist Richard Feynman in the 1940s. He developed them as a tool to simplify and visualize complex mathematical equations in quantum electrodynamics.

3. How do I read a Feynman diagram?

In a Feynman diagram, particles are represented by lines and interactions between particles are shown as points where the lines meet. The direction of the lines represents the flow of time, with arrows pointing towards the future. The diagram also includes mathematical symbols and equations to describe the properties of the particles and their interactions.

4. What do the different types of Feynman diagrams represent?

There are several types of Feynman diagrams, each representing a different type of interaction between particles. For example, a vertex diagram represents the interaction between three particles, while a loop diagram shows the self-interaction of a single particle. The type of diagram used depends on the specific situation and calculation being done.

5. How do I create a Feynman diagram?

To create a Feynman diagram, one must first understand the mathematical equations and principles behind the interactions being studied. Then, using the appropriate rules and symbols, the diagram can be constructed by hand or with the help of a computer program. It requires a good understanding of quantum field theory and particle physics to accurately create and interpret Feynman diagrams.

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