Geometry, field, state, and normalization

The covariance convention is recorded explicitly to avoid a transpose ambiguity. If $K=W_0\mathrm{diag}({\lambda }_a){W_0}^{†}$, the finite-packet density operator is

where ${\Gamma }_{\mathrm{s}}$ is bosonic second quantization. Diagonalizing $K$ reduces (eq:gaussian) to geometric oscillator densities of mean ${\lambda }_a$. This is the finite-packet state construction recorded in En02-E CheungEn02E ({thm:gaussian}); it is not a dynamical backreaction result.