I am not really sure how this Fock space picture in QFT would port to curved spacetime, but in QFT, you can form a state that has particles of some momentum, with their spacetime information spread out (infinite variance) or unspecified.

In curved spacetime though, metric tensor differs from spacetime points to another. How would this state of particles of definite momenta be maintained in QFT in curved spacetime?

  • $\begingroup$ I looked up this topic (basic QFT in curved spacetime) and found this article (arxiv.org/pdf/1401.2026.pdf) co-written by Robert Wald. The free Klein-Gordon Fock space is constructed starting on page 11. I'm reading through it now. $\endgroup$ – Arturo don Juan Mar 13 '18 at 17:09
  • $\begingroup$ Short answer: it doesn't. The Klein-Gordon operator still has a basis of eigenfunctions called modes, but those aren't plane waves anymore. Consequently, the notion of elementary particles changes dramatically (AFAIK some textbook authors claim it even ceases to make any sense). $\endgroup$ – Prof. Legolasov Mar 13 '18 at 22:22

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