Handling Static Fields in QFT: Exploring Limitations and Solutions

In summary, the conversation discusses the concept of static fields and how they can be handled in quantum field theory (QFT). It is mentioned that static fields do not necessarily require QFT, but the individual is still interested in understanding how QFT approaches this scenario. The idea of using a limit for low frequencies is suggested. The conversation then delves into the exchange of virtual field quanta and how they can possess negative momentum, which may be causing the individual's confusion. Examples are given of how electrons and protons exchange quanta in different scenarios.
  • #1
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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
 
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  • #2
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 :)
 
  • #3


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.

 

1. What is a static field in quantum field theory?

A static field in quantum field theory is a field that does not change over time. It is a fundamental concept in QFT, where fields are used to describe the behavior of particles and their interactions.

2. What are the limitations of handling static fields in QFT?

One limitation is that static fields violate the principle of locality, which states that interactions between particles can only occur at points in space and time. This can lead to mathematical inconsistencies and difficulties in making predictions.

Another limitation is that the vacuum state in QFT, which is the state with no particles present, is unstable when static fields are present. This can lead to vacuum decay and the production of new particles, making calculations more complex.

3. How can the limitations of handling static fields be addressed?

One solution is to introduce a regulator, which is a mathematical device used to regulate the behavior of the fields and make calculations more manageable. Another solution is to use renormalization techniques, which involve redefining the physical parameters of the theory to account for the effects of the static fields.

Additionally, some researchers have proposed modifying the fundamental equations of QFT to include the effects of static fields, such as by incorporating non-local interactions.

4. What are the potential implications of handling static fields in QFT?

The implications of handling static fields in QFT are still being explored and debated. Some researchers argue that it may lead to a more complete and accurate understanding of particle interactions, while others believe it may introduce new theoretical and mathematical challenges.

It is also possible that handling static fields could have practical implications, such as in the development of new technologies or in the study of cosmological phenomena.

5. How does the study of handling static fields in QFT relate to other fields of physics?

The study of handling static fields in QFT is closely related to other fields, such as high energy physics, cosmology, and quantum gravity. It also has implications for our understanding of the fundamental laws of physics and the behavior of matter and energy at the smallest scales.

Moreover, the challenges and solutions in handling static fields in QFT may have broader implications for the study of complex systems and the development of mathematical tools in other areas of science and engineering.

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