I have just gone through chapter 14 on the(adsbygoogle = window.adsbygoogle || []).push({}); QFT for the gifted amateur byLancaster and Blundell. Quantising the electromagnetic field results in the Hamiltonian:

$$\hat{H}=\int d^3p \sum^{2}_{\lambda=1} E_p \hat{a}^\dagger_{p\lambda} \hat{a}_{p\lambda}$$

with ##E_p=|p|##. In this post ##p## represents the momentum 3-vector.

My question is; how does the concept vacuum energy apply here? I think what is puzzling me is the fact that I see many authors arrive at this result:

$$\hat{H}=\sum_{p\lambda}\hbar \omega_p (\hat{a}^\dagger_{p\lambda}\hat{a}_{p\lambda}+\frac{1}{2})$$.

Also, the previous expression has an integration over ##p## as opposed to a sum.

Maybe I am comparing it to the wrong Hamiltonian, but I think that after applying normal ordering I get rid of the 1/2 term.

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# A Canonical quantisation of the EM field

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