Hi can anyone tell me why in the fermionic number operator case:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]<0|N/V|0>= \sum_{\pm r}\int d^3 k a^{\dagger}(t,r)a(t,r) [/itex]

because if:

[itex] N=a^{\dagger}(t,k)a(t,k) [/itex]then after fourier decomposition surely one gets:

[itex] \int d^3 r d^3 r \frac{1}{(2Pi)^{3}} a^{\dagger}(t,r)a(t,rk) [/itex]

and when fourier decomposing back i dont see how one can get the creation/annhilation operators as a function of r or how to get this sum term or the [itex] d^3k [/itex] term. This V term gives just a [itex] \frac{1}{V} [/itex] term in the final integral.

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# Number operator help

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