Coherent-state oscillator vacuum-energy convention
= Coherent-state oscillator vacuum-energy convention
An ordinary normal-ordered coherent-state Gaussian for energy $\varepsilon a^\dagger a$ gives $(1-e^{-\beta\varepsilon})^{-1}$. The physical oscillator with zero-point energy $\varepsilon/2$ requires the factor $e^{-\beta\varepsilon/2}$. A symmetric determinant prescription may encode that factor implicitly; it must not be counted twice.