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Sometimes I see the calculation of the vacuum energy written as:

[tex]\int\frac{d^3k}{(2\pi)^3}(k^2+m^2)[/tex]

and sometimes written:

[tex]\int\frac{d^4k}{(2\pi)^4}log(k^2+m^2)[/tex]

See for example http://arxiv.org/abs/hep-ph/0105021 equation9.

Does anyone know why you can increase the k integral power by one and why this introduces a log???

Thanks!!

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# Vacuum modes

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