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I am reading QFT in curved spacetime. In this book Wald writes that if the spacetime is stationary, there is a natural "particle interpretation" even if we have no positive frequency wave planes. As we have stationarity when we have a Killing field he uses the Lie derivative along it to get positive eigenvalues and to build a Fock space.

What happens if we take another Killing field? Would we get another equivalent Fock space?

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  • $\begingroup$ I think that the case of Minkowski spacetime does not help. Its isometry groups are described by Lorentz transformations (with associated killing vectors). they all map positive energy plane waves to positive energy plane waves. the constructed Fock spaces can be identified. $\endgroup$ – Naima Feb 19 '17 at 10:20
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This is an interesting question. Flat space has the usual Killing vector $\partial_t$, but Rindler coordinates also come with a natural Killing field corresponding to the time coordinates of uniformly accelerated observers. The transformation between the two Fock spaces is quite non-trivial as the accelerated observers see the Unruh effect radiation.

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