Hello everyone. What it the result for a Gaussian functional integral when the "matrix" is nothing but a number? Mathematically speaking is the following true?(adsbygoogle = window.adsbygoogle || []).push({});

$$

\int \mathcal{D}\phi e^{-\int d^3k f(k) |\phi(k)|^2}\propto \left(f(k)\right)^{-1/2}

$$

Here ##f(k)## is just a function of k, not derivatives or operators etc... I'm asking this because in principle we should have a determinant of the "matrix" and I don't know if what I wrote is correct.

Thanks!

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# Gaussian functional integral with constant operator

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