Thanks for linking, your notes look really good vanhees71!
Would this be a fair summary for the Heat-Kernel method (starting on page 93 of the linked notes)?
If we call the operator we're interested in H.
Work out the propogator ## \langle x | exp(- H \theta) | x' \rangle ##
Then get some kind...
So in particular, how could the determinant of some general "operator" like
$$ \begin{pmatrix}
f(x) & \frac{d}{dx} \\ \frac{d}{dx} & g(x)
\end{pmatrix} $$
with appropriate boundary conditions (especially fixed BC), be computed? And assuming that it diverges, would it be valid in a stationary...