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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

[tex]

\hat H=\frac{1}{2}\int d^{n-1}k[\hat n_k+\frac{1}{2}\delta^{n-1}(0)]\omega

[/tex]

and then letting it act on a ground state, such that [itex]\hat n_k |0\rangle=0|0\rangle[/itex]

and so

[tex]

\hat H|0\rangle=\frac{1}{4}\int d^{n-1}k\delta^{n-1}(0)\omega=\frac{1}{4}\sum_k\omega

[/tex]

and putting a [itex]\omega_{max}[/itex] should get the result.

Now i as 2 things:

1) what precisely are the [itex]k,\omega[/itex] termu in the integration? I mean, they doesen't seem to be component of the four vector [itex]k^\mu=(\omega,\vec{k})[/itex]!

2) explicitly, how does the result is obtained?

thanks!!!!!

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# Vacuum energy calculation

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