How is the Power Spectrum of Matter Density Field Defined?

[SherLOCKed]

Homework Statement

The definition of power spectrum of matter density field is given by eq (1). I have also seen definitions of power spectra given by eq (2) . Does this mean $(2\pi^3)$ has been absorbed in the correlation function?

Relevant Equations

$P_{xx}(k)=(2\pi^3)\delta(k-k^\prime)\langle x(k)x(k^\prime)\rangle$

$P_{yy}(k)=\delta(k-k^\prime)\langle y(k)y(k^\prime)\rangle$

<Mentor: edit latex>

The definition of power spectrum of matter density field is given by eq(1). I have also seen definitions of power spectra given by eq(2) . Does this mean (2\pi^3) has been absorbed in the correlation function?

$$P_{xx}(k)=(2\pi^3)\delta(k-k^\prime)<x(k)x(k^\prime)>$$ .. (1)
$$P_{yy}(k)=\delta(k-k^\prime)<y(k)y(k^\prime)> $$.. (2)

 

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