- #1

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## Homework Statement

Hey guys,

So I have to show the following:

[itex][P^{\mu} , \phi(x)]=-i\partial^{\mu}\phi(x)[/itex],

where

[itex]\phi(x)=\int \frac{d^{3}k}{(2\pi)^{3}2\omega(\vec{k})} \left[ a(\vec{k})e^{-ik\cdot x}+b^{\dagger}(\vec{k})e^{ik\cdot x} \right][/itex]

and

[itex]P^{\mu}=\int \frac{d^{3}k}{(2\pi)^{3}2\omega(\vec{k})} k^{\mu} \left[ \mathcal{N}_{a}(\vec{k})+\mathcal{N}_{b}(\vec{k}) \right][/itex]

## Homework Equations

[itex]\mathcal{N}_{a}=a^{\dagger}(\vec{k})a(\vec{k})[/itex]

[itex]\mathcal{N}_{b}=b^{\dagger}(\vec{k})b(\vec{k})[/itex]

## The Attempt at a Solution

So all I've done is calculated the commutator as normal and collected all the terms, and I've got:

The only difference is that I've dropped the functional dependence on k to make it shorter.

I'm stuck at this point - not quite sure how to proceed! please help!!