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**[SOLVED] Klein-Gordon Causality calculation**

## Homework Statement

In Peskin and Schroeder on page 27 it is stated that when we compute the Klien-Gordon propagator in terms of creation and annihilation operators the only term that survived the expansion is

[tex]

<0|a_{\textbf{p}}a^{\dagger}_{\textbf{q}}|0> \ \ (1).

[/tex]

I am unsure of why the term

[tex]

<0|a^{\dagger}_{\textbf{p}}a^{\dagger}_{\textbf{q}}|0>

[/tex]

would vanish.

## Homework Equations

The expansion of the field is given by

[tex]

\phi (x) = \int \frac{d^{3}p}{(2 \pi)^{3}} \frac{1}{\sqrt{2E_{\textbf{p}}}}(a_{\textbf{p}}}e^{-ip\cdot x} + a^{\dagger}_{\textbf{p}}e^{ip\cdot x})

[/tex]

and the normalization condition for states is

[tex]

<\textbf{p}|\textbf{q}> = (2\pi)^{3}\delta^{3}(\textbf{p}-\textbf{q}).

[/tex]

## The Attempt at a Solution

Looking at the normalization condition given above I got,

[tex]

<0|a^{\dagger}_{\textbf{p}}a^{\dagger}_{\textbf{q}}|0> = <0|\textbf{p}+\textbf{q}> = (2\pi)^{3}\delta^{3}(\textbf{p}+\textbf{q}).

[/tex]

However this mean that (1) is not the only surviving term, and from my calculations this also gives a factor of 2 that should not be there. I am unsure of how this term vanishes.