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## Main Question or Discussion Point

Hi

I have a question regarding second quantization. In the following link: http://books.google.dk/books?id=v5v...q="The introduction of quantum field"&f=false (equation 1.71) they write the kinetic energy operator in real space representation, i.e. using quantum field operators. Here they rigourously transform the creation/annihilation operators using equation 1.69 the page before.

Now, if we take a look at equation 1.101 on page 24, they write the potential energy operator

My question is, why they do not make that rigourous transformation in the case with

I will appreciate any help you can give me.

Best,

Niles.

I have a question regarding second quantization. In the following link: http://books.google.dk/books?id=v5v...q="The introduction of quantum field"&f=false (equation 1.71) they write the kinetic energy operator in real space representation, i.e. using quantum field operators. Here they rigourously transform the creation/annihilation operators using equation 1.69 the page before.

Now, if we take a look at equation 1.101 on page 24, they write the potential energy operator

*V*in momentum space, but notice how they do not make the same rigourous transformation of the creation/annihilation operators, but merely substitute ν with k in equation (1.62) in their indices.My question is, why they do not make that rigourous transformation in the case with

**k**, but only change the indices of the operators. Can you shed some light on this?I will appreciate any help you can give me.

Best,

Niles.