Handling Static Fields in QFT: Exploring Limitations and Solutions

[lalbatros]

Hello,

I just realized that I could not figure out how static fields can be handled in QFT.
Although I realize that really static fields don't really need QFT, I nevertheless would like to see how QFT covers this extreme case. Maybe a limit for low frequencies would be useful.

Have you any idea about that?
Thanks,

Michel

 

[Mr.Brown]

you mean by static field something like a static electric field pulling on charges.
That case is solved by exchange of virtual field quanta which can also posses negative momentum ( i think that´s where your problem lies doesn´t it :) ? )

For example 2 electrons moving towards each other exchange one quanta of positive momentum while they are repelled from each other.
Two protons instead exchange one quanta of negative momentum while attrackted to each other.

Hope i could help you :)

 

[denian]

Hello Michel,

Thank you for bringing up this interesting topic. Handling static fields in QFT can indeed be a challenging task, as they do not exhibit the same behavior as dynamic fields. However, there have been several approaches proposed to address this issue.

One solution is to introduce a cutoff frequency in the theory, which essentially sets a limit for the low frequencies that can be described by QFT. This approach has been used in various models, such as the scalar field theory and the electromagnetic field theory, to handle static fields.

Another method is to incorporate the concept of renormalization, which involves adjusting the parameters of the theory to account for the effects of static fields. This approach has been successful in describing the behavior of static fields in QFT, but it can be quite complex and requires careful calculations.

Additionally, there have been attempts to modify the equations of QFT to explicitly include static fields. This has led to the development of theories such as the Stochastic Electrodynamics, which aims to explain the behavior of static fields through a stochastic process.

Overall, while QFT may not be the most natural framework for handling static fields, it has been shown to be capable of describing their behavior through various approaches. I hope this helps answer your question. Thank you.