N-point Green's function in QFT

Click For Summary

Discussion Overview

The discussion revolves around the role and necessity of N-point Green's functions in quantum field theory (QFT), particularly in relation to 2-point Green's functions. Participants explore the implications of using different formalisms, such as path-integral and canonical approaches, and the equations governing these functions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the necessity of N-point Green's functions if 2-point functions can suffice for certain calculations in both path-integral and canonical formalisms.
  • Another participant inquires about the specific equation that the 2-point Green's function satisfies in an interacting field theory.
  • Some participants express difficulty in finding the equation satisfied by the N-point Green's function, particularly when using perturbative expansions.
  • A later reply suggests that renormalizing the coupling constant may require the calculation of the 4-point function, indicating a potential need for higher-order functions.
  • There is mention of the S matrix and how N-point functions can be reduced to 2-point functions through Wick's contraction, while also considering symmetry factors and Feynman diagrams.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the necessity and equations of N-point Green's functions, indicating that multiple competing views remain on the topic.

Contextual Notes

Some participants highlight limitations in their understanding of the equations governing Green's functions, particularly in the context of perturbation theory and renormalization.

Who May Find This Useful

This discussion may be of interest to those studying quantum field theory, particularly in understanding the roles of different Green's functions and their applications in calculations.

Dyson
Messages
21
Reaction score
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?
 
Physics news on Phys.org
What is the equation satisfied by the 2-point Green's function in an interacting field theory?
 
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.
 
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. :)
 
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?
 

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 0 ·
Replies
0
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 21 ·
Replies
21
Views
5K