The Free-Field Variances of the Fourier Modes

In the setting of The Wick-Square Problem on the Torus: Standing Notation, the free-field variance of the mode $k\in\mathbb{Z}^{n}$ is the real number¶

$$c_{k}=\frac{\nu}{2\mu_{k}} ,$$

defined because $2\mu_{k}$ is positive: $\mu_{k}$ is positive by The Wick-Square Problem on the Torus: Standing Notation §modes, and a product of positive numbers is positive by claim 5 of Elementary Order Arithmetic in an Ordered Field. It is positive, by claims 7 and 5 of that lemma, because $\nu$ is positive (The Wick-Square Problem on the Torus: Standing Notation §parameters).