Vacuum state in a stationary spacetime

In a strictly stationary spacetime, the timelike Killing flow gives a preferred positive-frequency splitting. The corresponding vacuum is annihilated by every annihilation operator associated with a positive-frequency mode.

For one-particle Hilbert space ${\mathcal{H}}_1$, the bosonic Fock space isCreation operators add one symmetrized particle and annihilation operators remove one.