Vacuum state for an asymmetric space

Question

I am studying Bunch-Davies vacuum. In the derivation it is important the symmetry of the background space: the vacuum is the state which is invariant under the isometries of the space.
But what if the space had no symmetry? How could one pick a vacuum state?

Eric David Kramer · Answer

If there is no symmetry, there is in general no way to pick a vacuum state, because a state that is invariant under time translation in one set of coordinates is in general time-dependent in a different set of coordinates, and since there is no symmetry, there is no preferred coordinate system.

Answered by Eric David Kramer on July 19, 2021

Vacuum state for an asymmetric space

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