Consider the field being decomposed into a orthogonal and completed basis:
$\Phi(x) = \sum_n c_n \phi_n(x)$ (or $\Phi(x) = \int dk c_k \phi_k (x)$, if continuous)
The notation:
$\phi_n(x) = <x|\phi_n>$ (or $\phi_k = <k|\phi_n>$, if continuous)
The integration measure can be rewritten as:
$\mathcal{D}\Phi \sim \prod_n dc_n$
What is the proportional prefactor? In some literature, it is written as:
$(\det <n|\phi_n>)^{-1}$
But still, what does that mean? I mean, how one calculate it, or write it in function?
