N-point Green's function in QFT

Click For Summary
SUMMARY

The discussion centers on the necessity of N-point Green's functions in Quantum Field Theory (QFT) compared to 2-point Green's functions. Participants highlight that while 2-point functions can suffice for calculating transition amplitudes via Wick contractions, N-point functions are essential for comprehensive analyses, particularly in renormalization processes. The conversation also emphasizes the role of perturbative expansions in deriving equations satisfied by these functions, specifically in interacting field theories.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT) principles
  • Familiarity with Green's functions, particularly 2-point and N-point functions
  • Knowledge of Wick's theorem and contractions
  • Experience with perturbative expansion techniques in field theories
NEXT STEPS
  • Study the derivation and applications of N-point Green's functions in QFT
  • Explore the role of Feynman diagrams in calculating transition amplitudes
  • Investigate the process of renormalization and its dependence on 4-point functions
  • Learn about perturbative expansions and their implications in interacting field theories
USEFUL FOR

Physicists, particularly those specializing in Quantum Field Theory, graduate students studying advanced theoretical physics, and researchers focusing on particle interactions and renormalization techniques.

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

Graduate Which operator corresponds to the Green function in QFT?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate QFT Superposition of Final States
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Why "Green's function" is used more than "correlations" in QFT?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate What does "solving a quantum mechanics problem" mean?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Computing Correlation functions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Positive polarity of a retarded Green's function's imaginary part
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Importance of Densities in QFT
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How to know the number of Feynman diagrams for a given order?
  • · Replies 0 ·
Replies
0
Views
1K
Graduate Calculating nonequilibrium Green's Functions
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Path integral propagator as Schr's eq Green's function
  • · Replies 21 ·
Replies
21
Views
4K