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nicksauce

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## Main Question or Discussion Point

In equation 2.23 we have

[tex] \phi = \frac{1}{\sqrt{2\omega}}(a + a^{\dagger}) [/tex]

So how come equation 2.25 is

[tex] \phi(x) = \int{\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_pe^{ipx} + a_p^{\dagger}e^{-ipx})} [/tex]

And not

[tex] \phi(x) = \int{\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p + a_p^{\dagger})e^{ipx}} [/tex]

[tex] \phi = \frac{1}{\sqrt{2\omega}}(a + a^{\dagger}) [/tex]

So how come equation 2.25 is

[tex] \phi(x) = \int{\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_pe^{ipx} + a_p^{\dagger}e^{-ipx})} [/tex]

And not

[tex] \phi(x) = \int{\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p + a_p^{\dagger})e^{ipx}} [/tex]