# Vacuum energy calculation

1. Sep 6, 2011

### tunafish

Hi guys!!
I searchead a lot for this but i couldn't find in anywhere: what calculation is made to esimate the vacuum energy of a scalar field??

I red that it starts considering the Hamiltonian in the form
$$\hat H=\frac{1}{2}\int d^{n-1}k[\hat n_k+\frac{1}{2}\delta^{n-1}(0)]\omega$$
and then letting it act on a ground state, such that $\hat n_k |0\rangle=0|0\rangle$
and so
$$\hat H|0\rangle=\frac{1}{4}\int d^{n-1}k\delta^{n-1}(0)\omega=\frac{1}{4}\sum_k\omega$$
and putting a $\omega_{max}$ should get the result.

Now i as 2 things:
1) what precisely are the $k,\omega$ termu in the integration? I mean, they doesen't seem to be component of the four vector $k^\mu=(\omega,\vec{k})$!

2) explicitly, how does the result is obtained?

thanks!!!!!