- #1
waht
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Homework Statement
Ok so got a solution to the Klein-Gordon equation and need to solve for a(k)
\varphi(x) = \int \tilde{dk} \left[ a(\bold{k}) e^{ikx} + a^{\dagger}(\bold{k} ) e^{-ikx} \right]
\tilde{dk} = \frac{d^{3}k}{(2 \pi)^{3} 2 \omega}
The way it's done in Srednicki p.26 has me confused when taking the Fourier transform of \varphi
\int d^3x e^{-ikx} \varphi(x) = \frac{1}{2\omega} a(\bold{k}) + \frac{1}{2\omega} e^{2i\omega t} a^{\dagger}(\bold{-k} )
Homework Equations
kx = \bold{k} \cdot \bold{x} - \omega t
The Attempt at a Solution
\int d^3x e^{-ikx} \varphi(x) =\int d^3x e^{-ikx} \int \tilde{dk} \left[ a(\bold{k}) e^{ikx} + a^{\dagger}(\bold{k} ) e^{-ikx} \right]
= \int d^3x \int \tilde{dk} a(\bold{k}) + \int d^3x \int \tilde{dk} e^{-2kx} a^{\dagger}(\bold{k} )
so the problem is how do these integrals with respect to dx and dk disappear?
