Treating Mass as a perturbation

In summary, the conversation discusses the topic of the Klein-Gordon equation and the use of a perturbation model to calculate transition amplitudes. The Feynman diagram shows the interaction point via the perturbation, which is modeled as a potential. The self energy of a relativistic particle can be treated as a perturbation or potential, leading to a change in mass and charge that is attributed to it. This concept is further explained in Sakurai's book "Advanced Quantum Mechanics".
  • #1
Sekonda
207
0
Hello again,

I also have another question, somewhat related to my previous, on the topic of the Klein-Gordon equation but treating the mass as a perturbation.

The feynman diagram shows the particular interaction:

feynman2.png


I believe the cross is the point of interaction via the perturbation (the mass), we model the perturbation:

[tex]\delta V=m^2[/tex]

and subsequently use this in the calculation for the transition amplitude, we use plane-wave solutions of the ingoing and outgoing states.

Alike to my previous question, I'm not really sure what this means to model some potential as a mass? Can anyone explain why we do this and maybe exactly what is happening in this particular feynman diagram?

I can try to embelish if needs be, please tell me if there are any inconsistencies or errors I have made in my explanation of my problem!

Thanks,
SK
 
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  • #2
The self energy of a particle is the contribution to the particles energy due to interactions with the system. Considering we are dealing with a relativistic particle, is this self energy the invariant mass term in the relativistic energy-momentum relation and thus can be treated as the perturbation/potential of the system or interaction?
 
  • #3
self energy contribution is repalced by a change in mass which is attributed to it.It helps to redefine the masses and charges by renormalized charge and mass.you can see sakurai 'advanced quantum mechanics' for why this can be treated as a mass change.
 

1. What is the concept of treating mass as a perturbation?

Treating mass as a perturbation is a mathematical technique used in physics to simplify complex systems by breaking them down into smaller, more manageable pieces. In this approach, the mass of an object is treated as a small disturbance or perturbation in an otherwise idealized system. This allows for easier calculations and predictions of the behavior of the system as a whole.

2. What types of systems can be treated as perturbations?

Any system that contains a small parameter, such as mass, can be treated as a perturbation. This includes physical systems such as atomic and molecular structures, electromagnetic fields, and gravitational fields. It can also be applied to abstract systems, such as economic models or biological systems.

3. What are the advantages of treating mass as a perturbation?

By treating mass as a perturbation, we can simplify complex systems and make them more manageable to study. This approach allows us to make predictions and calculations that would be too difficult or impossible to do without breaking down the system into smaller parts. It also helps us to understand the behavior of the system and how different parameters, such as mass, affect its overall behavior.

4. Are there any limitations to treating mass as a perturbation?

Treating mass as a perturbation can be a useful tool, but it does have its limitations. This method is most effective when the perturbation (mass) is small compared to the other parameters in the system. If the perturbation is too large or if there are multiple perturbations, this approach may not accurately predict the behavior of the system.

5. How is treating mass as a perturbation used in practical applications?

The concept of treating mass as a perturbation is used in many practical applications in physics and engineering. For example, it is commonly used in quantum mechanics to study the behavior of particles, in fluid dynamics to analyze the flow of fluids, and in astrophysics to study the motion of celestial bodies. It is also used in the design and analysis of structures and systems, such as bridges and aircraft, to predict their behavior under different conditions.

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