Expressing Feynman Green's function as a 4-momentum integral

In summary, the conversation discusses the use of (z',p) as a 4-vector and the confusion surrounding its interpretation. The speaker questions the validity of using a new variable in forming a 4-vector with momentum and the change in interpretation of z' as a result. The conversation also mentions the use of ##\theta(x^0 - y^0)## and its preservation of time orientation in the restricted Lorentz group. The rest of the conversation involves expressing this in momentum space.
  • #1
realanswers
13
0
Homework Statement
N/A
Relevant Equations
N/A
1678463170187.png


I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do not see how this is okay. The interpretation of z' now is different.
 
Physics news on Phys.org
  • #2
realanswers said:
I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do not see how this is okay. The interpretation of z' now is different.
But where did it come from? ##\theta(x^0 - y^0)##, right? The restricted Lorentz group (identity-connected part) preserves time orientation, so it's ok to use ##\theta(x^0 - y^0)## in that circumstance. The rest just involves expressing it in momentum space.
 
  • Like
Likes vanhees71

1. What is Feynman Green's function?

Feynman Green's function is a mathematical tool used in quantum field theory to describe the propagation of particles in space and time. It is a solution to the Feynman propagator equation and helps calculate the probability amplitude for a particle to move from one point to another in spacetime.

2. Why is it important to express Feynman Green's function as a 4-momentum integral?

Expressing Feynman Green's function as a 4-momentum integral allows for a more efficient and elegant way to solve complex problems in quantum field theory. It also allows for a better understanding of the behavior of particles in spacetime and helps in the calculation of scattering amplitudes.

3. How is Feynman Green's function related to quantum mechanics?

Feynman Green's function is a key concept in quantum mechanics as it helps describe the behavior of particles at the quantum level. It is used to calculate the probability amplitude of a particle to move from one point to another in spacetime, which is a fundamental concept in quantum mechanics.

4. Can Feynman Green's function be applied to all types of particles?

Yes, Feynman Green's function can be applied to all types of particles, including fermions and bosons. It is a universal tool in quantum field theory that can be used to describe the behavior of particles regardless of their type or properties.

5. Are there any limitations to expressing Feynman Green's function as a 4-momentum integral?

While expressing Feynman Green's function as a 4-momentum integral is a powerful and widely used technique, it may not always be the most efficient method for solving certain problems in quantum field theory. In some cases, alternative methods may be more suitable or necessary to obtain accurate results.

Similar threads

Replies
1
Views
808
  • Advanced Physics Homework Help
Replies
1
Views
1K
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Differential Equations
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
9
Views
2K
Replies
3
Views
743
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
3K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Back
Top