N-point Green's function in QFT

In summary, the N-point Green's function is introduced in QFT to calculate the transition amplitude in both the path-integral and canonical formalisms. While the 2-point Green's function can be calculated in both formalisms, the N-point Green's function is necessary for interacting field theories. The equation satisfied by the 2-point Green's function in an interacting field theory can be found using perturbative expansion and the definition of N-point Green's function. When renormalizing the coupling constant, the 4-point function must be calculated. In calculating the S matrix, N-point functions can be reduced to 2-point functions using Wick's contraction, with symmetry factors accounted for by Feynman diagrams.
  • #1
Dyson
21
0
Hello!
Something about N-point Green's function in QFT really troubles me...
In the path-integral formalism,why will we introduce the N-point Green's function? I mean is it enough because we have calculated the 2-point green's function.
And in the canonical formalism, it seems we can finish the calculation of transition amplitude only with the help of 2-point Green's function(Wick contraction)
What are the differences?
 
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  • #2
What is the equation satisfied by the 2-point Green's function in an interacting field theory?
 
  • #3
Using the pertubative expansion and the definition of N-point Green's function.Because of the pertubation,i can only calculate the 2-point Green's function.But i really can't find the equation it satisfies.
 
  • #4
Dyson said:
Using the pertubative expansion and the definition of N-point Green's function.Because of the pertubation,i can only calculate the 2-point Green's function.But i really can't find the equation it satisfies.

Funny, because it carries your name. :)
 
  • #5
Please correct me if I'm wrong, but when we renormalize the coupling constant, don't you need to calculate the 4point function?

And in calculating the S matrix, you can get some N point function, which has to be reduced to 2 point functions using Wick's contraction, but with all sorts of symmetry factors which you use Feynman diagrams to account for?
 

1. What is an N-point Green's function in QFT?

An N-point Green's function in quantum field theory (QFT) is a mathematical tool used to calculate the probability amplitude for a particle to travel from one point to another in a quantum field. It takes into account all possible interactions between the particles in the field and is an essential component in perturbative calculations in QFT.

2. How is the N-point Green's function calculated?

The N-point Green's function is calculated using the Feynman path integral approach, which involves summing over all possible paths that a particle can take between the initial and final points. This includes integrating over all possible momenta and energies for the particles involved in the interaction. The resulting expression is then simplified using Feynman diagrams.

3. What is the significance of the N-point Green's function in QFT?

The N-point Green's function plays a crucial role in perturbative calculations in QFT. It allows for the calculation of scattering amplitudes and cross-sections, which are essential in understanding the behavior of particles in quantum fields. It also provides a framework for studying quantum field theories and their predictions.

4. How does the N-point Green's function relate to other concepts in QFT?

The N-point Green's function is closely related to other important concepts in QFT, such as the Feynman propagator, which describes the propagation of a particle through a field. It is also related to the S-matrix, which represents the transition probability for particles between initial and final states. Additionally, the N-point Green's function is connected to the vacuum expectation value, which represents the average value of an operator in the vacuum state.

5. What are some applications of the N-point Green's function in QFT?

The N-point Green's function has many practical applications in QFT, such as in the calculation of cross-sections for particle interactions in high-energy physics experiments. It is also used in the study of phase transitions and critical phenomena, as well as in the calculation of physical observables in condensed matter systems. Additionally, the N-point Green's function is essential in the development of new quantum field theories and in understanding the behavior of matter at a fundamental level.

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