General Gauge Invariance Problem

In summary, the conversation discusses the process \gamma \gamma \to W^+ W^- and the gauge independence of its amplitude. The speaker uses general expressions for propagators and vertices to calculate 5 diagrams, including one with a non-physical field \phi. They are unsure how to eliminate gauge dependence in the final expressions and ask for help understanding the role of the unphysical field \phi.
  • #1
llorgos
20
0
Hi!

I have to prove that the amplitude of the process

[itex]\gamma \gamma \to W^+ W^- [/itex]

does not depend on the gauge we will choose, [itex]R_{\xi}[/itex].

So I use the most general expressions for the propagators and vertices. I find 5 diagrams. One that involves only the 4 fields and a vertex, 1 t and one u channel with a W boson as propagator and 1 t and 1 u where the propagator is a non-physical field [itex]\phi[/itex].

I just sum up the last 4, since the first one does not depend on the [itex]\xi[/itex] parameter but then I am stuck since nothing seems to make the horrible expressions in such a way that there will be no gauge dependence in the end..

Any help?
 
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  • #2
llorgos said:
non-physical field [itex]\phi[/itex].

What is this unphysical field? - A ghost? If it is, I don't see how you make the diagram. If it's some field I don't know, please elaborate.
 
  • #3
It is a goldstone boson coming around in the [itex]R_{\xi}[/itex] gauge. Actually it is the charged one.
 

What is the General Gauge Invariance Problem?

The General Gauge Invariance Problem, also known as the Gauge Invariance Problem or the Gauge Problem, is a fundamental issue in theoretical physics. It refers to the fact that certain theories, such as quantum field theories, possess an infinite number of equivalent mathematical descriptions or "gauge transformations". This leads to difficulties in interpreting physical quantities and making predictions.

Why is the General Gauge Invariance Problem important?

The General Gauge Invariance Problem is important because it affects the way we understand and interpret physical theories. It also has practical implications for making accurate predictions in certain areas of physics, such as quantum electrodynamics and quantum chromodynamics.

How is the General Gauge Invariance Problem addressed?

There are a few different approaches to addressing the General Gauge Invariance Problem. One approach is to choose a specific gauge, or mathematical description, that simplifies the theory and makes physical quantities easier to interpret. Another approach is to use mathematical techniques, such as the Faddeev-Popov method, to eliminate the extra degrees of freedom caused by gauge transformations.

What are some potential solutions to the General Gauge Invariance Problem?

Some potential solutions to the General Gauge Invariance Problem include the Higgs mechanism, which gives particles mass and breaks gauge symmetry, and the concept of renormalization, which allows physicists to make meaningful predictions despite the infinite number of gauge transformations. Other theories, such as string theory, also attempt to address the problem in different ways.

How does the General Gauge Invariance Problem impact our understanding of the universe?

The General Gauge Invariance Problem impacts our understanding of the universe in a few ways. Firstly, it highlights the limitations of our current theories and the need for further research and development. Secondly, it challenges our traditional notions of causality and determinism, as gauge transformations can change the values of physical quantities without affecting the final outcome. Lastly, it raises philosophical questions about the nature of reality and whether our mathematical descriptions are truly reflective of the fundamental laws of the universe.

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