Positive-frequency solution

Relative to a timelike Killing field $K$, a positive-frequency solution obeys $i{\mathcal{L}}_{K}u=\omega u$ with $\omega >0$. Such solutions define the one-particle space and annihilation operators of a stationary vacuum.

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.