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In Wikipedia

https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem?wprov=sfti1

It states that

“The proof requires the following assumptions:

  1. The theory has a Lorentz-invariant Lagrangian.

  2. The vacuum is Lorentz-invariant.

  3. The particle is a localized excitation. Microscopically, it is not attached to a string or domain wall.

  4. The particle is propagating, meaning that it has a finite, not infinite, mass.

  5. The particle is a real excitation, meaning that states containing this particle have a positive-definite norm.”

So the question is Whether there is a generalization of it in curved spacetime?

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1 Answer 1

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I believe there is such a book about this generalization of spin statistics in curved spacetime:

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A gene ralization is proposed in which locally covariant theories are defined a s functors from a category of framed spacetimes to a category of ∗ -algebras. This allows for a more operational description of theories with s pin, and for the derivation of a more general version of the spin-statist ics connection in curved spacetimes than previously available. The proof i nvolves a “rigidity argument” that is also applied in the standard set ting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to ge neral curved spacetimes.

Please see the citation here:

https://arxiv.org/pdf/1503.05797.pdf

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