- #1
Dixanadu
- 254
- 2
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!