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Symmetries in QFT

Physics Asked on September 2, 2021

There are very famous Coleman–Mandula theorem and Haag–Łopuszański–Sohnius theorem , see also this and this.

It states that "space-time and internal symmetries cannot be combined in any but a trivial way".

But this theorem didn’t give any restrictions on internal symmetry group. Which symmetries can be realised in QFT?
What about Quantum group, Hopf algebra? Or maybe more exotic algebras?

Which internal symmetries one can realise in QFT?

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