Question on Montonen-Olive duality

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In summary, the Montonen-Olive duality states that two classical theories can give rise to the same QFT. This can occur when a classical theory of electrically charged particles leads to a magnetic monopole and a classical theory of magnetic monopoles leads to a composite charged particle, both as limits of one QFT. The literature explains that the first theory is obtained by taking the h->0 limit with the magnetic charge held fixed, while the second theory is obtained by taking the h->0 limit with the electrical charge held fixed. This is a matter of convenience in terms of which charge is considered the more dominant in the perturbation theory.
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metroplex021
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Hi folks,

I've been reading about Montonen-Olive duality and understand that two different classical theories can give rise to the same QFT. In particular, we can have a classical theory of electrically charged particles giving rise to a magnetic monopole, and a classical theory of magnetic monopoles giving rise to a composite charged particle -- and have these both as limits of one QFT. The literature on this issue makes clear that the first theory will be the h->0 limit of the QFT with the magnetic charge held fixed, and the second theory will be the h->0 limit of the QFT with the electrical charged held fixed.

But what I don't understand is *why* it is that, when we have a theory of electrically charged particles we regard h as a function of charge and hold the magnetic charged fixed when taking the limit; and vice versa for the theory of magnetic charges. Can anyone give me even a qualitative explanation of why this is the case? I'd appreciate it very much!

Thanks
 
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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 
  • #3
It is more of a philosophical question rather than a real science question. It is actually a matter of convenience in which you want to treat it.

If for example you are doing Feynman diagram, then you should better keep track with electrical charge because it is small and your perturbation theory will do fine. However if you want to use magnetic charge, then your coupling strength will be higher ( in case you just use Dirac quantization condition), and your perturbation theory will break down. Both are equally correct, but it is a matter of convenience.
 

1. What is Montonen-Olive duality?

Montonen-Olive duality, also known as S-duality, is a theoretical concept in particle physics that suggests the strong and weak nuclear forces may be equivalent to each other at high energies. This means that a theory describing the strong force can also describe the weak force, and vice versa.

2. Who were Montonen and Olive?

Montonen and Olive were two physicists who proposed the concept of duality in 1977. They were studying the mathematical relationship between gauge theories and discovered that under certain conditions, the equations describing the strong and weak forces could be transformed into one another.

3. How is Montonen-Olive duality related to string theory?

String theory is a theoretical framework that attempts to describe all fundamental particles and forces in the universe as tiny vibrating strings. Montonen-Olive duality is a key component of string theory, as it helps to reconcile the different types of forces in the theory and provides a unified description of the universe.

4. Is Montonen-Olive duality a proven concept?

No, Montonen-Olive duality is still a theoretical concept and has not been proven experimentally. However, it has been extensively studied and is widely accepted by physicists as a promising idea that may help to unify our understanding of the fundamental forces in the universe.

5. What are the potential implications of Montonen-Olive duality?

If Montonen-Olive duality is proven to be true, it would have major implications for our understanding of the universe. It could help to explain the relationship between the different forces and particles, and could potentially lead to a more complete theory of everything that unifies all of physics.

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