Integrated kernel and spectral zeta function

1. Aug 25, 2010

grilo

I was looking at a paper about strong-coupling expansion (N. F. Svaiter, Physica (Amsterdam) 345A, 517 (2005) ) and it claims that
$$-\int d^d x \int d^d y (-\Delta + m^2)\delta^d(x-y) = \textbf{Tr} I + \left.\frac{d}{ds}\zeta(s)\right|_{s=0}$$
where $$\zeta(s)$$ is the spectral zeta function, and $$I$$ is the identity matrix.

It is clear to me that the derivative of the zeta function is related to the logarithm of the determinant of the operator in the left-hand side. What is *not* clear is how that double integral is related to that.