# Can QFT be constructed without using vacuum?

So my question is simple when doing QFT in classical curved spacetime we found out that we have different sets of complete functions which leads to different vacuum states. And these different vacuum states actually leads to the fact that we observe particles at a different time or in a different frame depending on the situation. Therefore I want to ask people who deal with axiomatic QFT that can we use some concept other than vacuum to deal with QFT in curved spacetime. But abandoning vacuua concept is same as not using Fock space because without vacuua we can't guarantee that our energy operator is bound from below.

• I don't know an explicit, definitive proof that it can't, but it seems unlikely. IMO this is exactly why QFT in curved spacetime is difficult; read about e.g. the Unruh effect (en.wikipedia.org/wiki/Unruh_effect). Dec 2, 2019 at 10:43
• @MartinC. Actually in Unruh effect there is no issue of curvature. The spacetime is flat if we negelect the back reaction which is assumed by default. Unruh effect happens because of 2 different set of complete function and therefore 2 different vacuua. Dec 2, 2019 at 11:44
• I’m definitely not an expert in this field, so I’ll take your word for it. Dec 2, 2019 at 13:12
• The role of the vacuum in the formulation of QFT is to fix a representation of the CCR. Due to the infinite number of the degrees of freedom, the Stone-von-Neumann theorem doesn't apply to QFT and there are inequivalent representations on different Hilbert spaces. These representations all have Poincare-invariant states, but the one that contains the physical vacuum (the Fock representation for free theories) has its vacuum as the lowest-energy state. Dec 3, 2019 at 10:19