= Gaussian path integral
{c}
{title2=$\int\mathcal D\eta\,e^{i\langle\eta,A\eta\rangle}\propto(\det A)^{-1}$}
A quadratic <path integral> becomes a product of <Gaussian integrals> after diagonalizing its fluctuation operator. One real coordinate per mode gives an inverse square root of the <functional determinant>; one complex coordinate, or two real coordinates, gives its inverse. A regulator and normalization are essential: <determinant> ratios are often meaningful before an absolute <determinant> is defined.
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