Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

given a surface with metric $ g_{ab} $ i would like to evaluate the functional determinant of the Laplacian in the form

$ - \partial _{s} \zeta (0,E^{2})=\log\det( \Delta + E^{2}) $

then i need to evaluate the Theta function $ \Theta (t)= \sum_{n} \exp(-tE_{n})$ for $t >0$ real

since this is too hard :( my idea is to use the approximation

$ \Theta (t) = \frac{1}{(2\pi)^{d}} \int dpdx\exp(-tH(x,p)) $

with the Hamiltonian of the surface $ H(x,p)= \sum_{a,b}g^{a,b}(x)p_{a}p_{b} $ summation over indices $a$ and $b$ is assumed :)

my question is if this approximation for the 'Theta function' or Heat Kernel of the Laplacian of the surface is valid, i need the Theta function in order to evaluate the determinant of the Laplacian by zeta-regularization.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.