# I 'Normalisation' of Fourier Transforms in QFT

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1. Aug 1, 2017

### tomdodd4598

Hi there - just a quick question about Fourier transforms:

When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ${ \left( 2\pi \right) }^{ -d/2 }$ in front of the integral. This is useful, as wave-functions normalised in position-space are also normalised in momentum-space.

However, now I have moved onto QFT, and online notes and the textbook I'm using put different constants in front of the integrals, namely ${ \left( 2\pi \right) }^{ -d }$ in front of the integral over momenta, and simply $1$ in front of the integral over positions.

Is there any explanation for this, or is this purely definition? If the latter is the case, what is the use this definition has over the one used for transforming wave functions?