Divergence of the amplitude for a Feynman diagram

Nov 28, 2018

Raymont

1. The problem statement
In calculating the amplitude for the diagram[1], view 1.jpg.
[1] Voja Radovanovic, Problem Book Quantum Field Theory

2. Homework Equations
View 2.jpg.

The Attempt at a Solution

View 3.jpg.[/B]
Why the integrals is divergent? Why the other terms are finite?

Nov 28, 2018

Raymont

The physical significance of the results are not very clear, can anyone explain it?

What is the significance of the divergence of the amplitude for a Feynman diagram?

The divergence of the amplitude for a Feynman diagram is an important concept in quantum field theory. It refers to the behavior of the amplitude as the energy or momentum of the particles involved approaches infinity. This divergence can indicate the presence of new, undiscovered particles or interactions in the theory.

How does the divergence of the amplitude affect the predictions of a Feynman diagram?

The divergence of the amplitude can lead to inconsistencies and inaccuracies in the predictions of a Feynman diagram. This is because the divergent behavior at high energies or momenta can cause the amplitude to become infinite, making it difficult to make meaningful predictions about the physical system.

What is the role of regularization in dealing with the divergence of the amplitude?

Regularization is a technique used in quantum field theory to eliminate the divergences in the amplitude. It involves introducing a mathematical parameter that modifies the behavior of the amplitude at high energies or momenta, allowing for more accurate predictions to be made. However, the choice of regularization method can also affect the physical interpretation of the results.

Can the divergence of the amplitude be completely eliminated?

No, the divergence of the amplitude cannot be completely eliminated. This is because it is a fundamental aspect of quantum field theory and reflects the inherent uncertainties and limitations of our understanding of the physical world. However, through the use of regularization techniques, we can reduce the magnitude of the divergence and make more accurate predictions.

How does the divergence of the amplitude relate to renormalization in quantum field theory?

Renormalization is another important concept in quantum field theory that deals with the divergences in the amplitude. It involves adjusting the parameters of a theory to account for the infinite terms that arise in the amplitude. This allows for more meaningful and accurate predictions to be made, and is a crucial aspect of reconciling quantum field theory with experimental results.