Can anyone explain what does the author mean by the statement below?(adsbygoogle = window.adsbygoogle || []).push({});

Let’s take advantage of translational invariance in d dimensions, ##x_μ → x_μ + a_μ## , to Fourier decompose the scalar field:

## \phi(z,x^\mu)=e^{ik_\mu x^\mu} f_k(z) ##_{page 27 of this paper}

I don't understand the relation between the Fourier transform and translational invariance.

Thanks

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# A Fourier transform and translational invariance

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