# Klein-Gordon Feynman Green's Function

A massive scalar field $$\phi (x,t)$$ of mass $$m$$ in quantum field theory satisfies the Klein-Gordon equation:

$(\Box + m^2) \phi(x,t) = 0,$

where $$\Box$$ indicates the d'Alembert wave operator:

$\Box = -\dfrac{\partial^2}{\partial t^2} +\dfrac{\partial^2}{\partial x^2} + \dfrac{\partial^2}{\partial y^2} +\dfrac{\partial^2}{\partial z^2}.$

Find the Green's function of the Klein-Gordon operator in momentum space by Fourier transform. Note that $$k = (E,\vec{k})$$ is a vector with four components: the energy of a particle, and its three components of spatial momentum.

Notation: $$\text{abs}(\cdot)$$ denotes the Absolute value function.

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