How to derive eq.3.34 in Lancaster's QFT book for beginners?

[anklimekruk]

Homework Statement

How to derive eq.3.34 in Lancaster's book QFT for the gifted amateur

Homework Equations

$\hat H= \int d^3 p E_p\hat a\dagger_p\hat a_p$

The Attempt at a Solution

Comparing

 

[anklimekruk]

How to derive the relevant equation ?
By comparing it to eq 2.41 in the book:
$\hat H = \sum_{k=1}^N\hbar\omega_k (\hat a\dagger_k\hat a_k + 1/2)$
I think 3.34 is the integral version of 2.41

 

[anklimekruk]

I would like to know why my question is left without an answer nor a comment

 

[Ray Vickson]

I would like to know why my question is left without an answer nor a comment

If they are like me, they do not have easy access to that book and so would have nothing useful to say. Perhaps if you wrote out more context and detail some of us could, indeed, figure out what was happening. (Not guaranteed, but just maybe possible.)

 

[anklimekruk]

If they are like me, they do not have easy access to that book and so would have nothing useful to say. Perhaps if you wrote out more context and detail some of us could, indeed, figure out what was happening. (Not guaranteed, but just maybe possible.)

I wrote the question so that there is no need for the book

 

[Ray Vickson]

I wrote the question so that there is no need for the book

You mean we don't need to know what is the form of $E_p$ in the integral $\int d^3 p E_p a_p^+ a_p$?

 

[anklimekruk]

You mean we don't need to know what is the form of $E_p$ in the integral $\int d^3 p E_p a_p^+ a_p$?

Maybe $E_p$ is the Energie in the momentum which replaces $\hbar w_k$ in 2.41.There is no more explanation in the book for as much as I can see.
In my eyes it must be the notation for the integral version of the discrete case of eq 2.41.I must of course convince myself that it is mathematicaly correct.
More questions will surely arise.I am willing to offer the book to somebody who would like to help me on a regular basis.