'Normalisation' of Fourier Transforms in QFT

[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?

Thanks in advance.

 

[vanhees71]

It's just convention, and it's a nuissance. There are so many normalization conventions that I've sometimes the impression it exceeds the number of physicists using QFT ;-)). I think, it's good to stick to the conventions of the Review of Particle Physics since this is most common in the field

http://pdg.lbl.gov/2017/reviews/rpp2016-rev-kinematics.pdf