[QFT] Divergent Green's function?

The Lagrangian given is for a Dirac spinor with two complex components and I am asked to derive Feynman rules for this theory using standard methods. However, there is also a request to "classify the divergent Green's functions" which is causing confusion. Additional research on "divergent Green's functions" has not provided much information.
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nocloud
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Homework Statement



I am being asked to consider a Dirac spinor with two complex components and the following Lagrangian:

[tex]L = L_{Dirac}-\stackrel{g}{4}{(\psi\bar{\psi})^{2}}[/tex]

I am asked to derive the Feynman rules for this theory which I can do using the standard methods. However, I am also asked to "classify the divergent Green's functions". Can anybody tell me what this question wants me to do? I am drawing a bit of blank here and googling "divergent Green's functions" isn't leading to a whole lot of useful information.

Homework Equations





The Attempt at a Solution


 
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  • #2
I have not been able to attempt a solution here as I am not sure what the question is asking me to do.
 

1. What is a divergent Green's function in quantum field theory?

A divergent Green's function in quantum field theory refers to a mathematical quantity that describes the propagation of particles in a quantum field. It is often used to calculate the scattering amplitudes and other physical observables in quantum field theories, but it can become infinite or "divergent" in certain cases, leading to difficulties in interpreting the results.

2. Why do we encounter divergent Green's functions in quantum field theory?

The presence of divergent Green's functions in quantum field theory is a consequence of the inherent quantum nature of the theory. In quantum mechanics, the position and momentum of a particle are described by operators that do not commute, leading to uncertainty in their measurements. This uncertainty can lead to divergences in certain calculations, such as those involving virtual particles or interactions at very small distances.

3. How do we deal with divergent Green's functions in quantum field theory?

There are several methods for dealing with divergent Green's functions in quantum field theory, such as regularization and renormalization. These techniques involve introducing a regulator to tame the divergences and then adjusting the parameters of the theory to remove the remaining infinities. This allows us to obtain meaningful physical predictions from the theory.

4. Can we avoid divergent Green's functions in quantum field theory?

In general, it is not possible to completely avoid divergent Green's functions in quantum field theory. However, in certain theories with special symmetries or in specific physical scenarios, the divergences may cancel out, leading to finite results. This is known as a "renormalizable" theory, and it is highly desirable in quantum field theory as it simplifies the calculations and makes the physical predictions more reliable.

5. What are the implications of divergent Green's functions in quantum field theory?

The presence of divergent Green's functions in quantum field theory can have significant implications for our understanding of the physical world. For example, it can lead to the need for new physics beyond our current theories, such as a theory of quantum gravity that can handle these infinities. It also highlights the nontrivial nature of quantizing gravity and the challenges that lie ahead in unifying quantum mechanics and general relativity.

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