# Canonically Conjugate meaning

1. Dec 6, 2012

### nateHI

Momentum and position are canonically conjugate in physics because they are the fourier transforms of each other.

In the context of abstract algebra what would that mean. More precisely, Let G be the group they both (p and x) belong to and let ψ:G->G/H be the natural homomorphism where H is the kernel of ψ. Would p and x be in the same coset in the set of cosets G/H?

Dang, I lost my train of thought and I'm not sure where I'm going with this now. I guess my question now is, please relate canonically conjugate in group theory to Fourier transforms.

Thanks, Nate

Last edited: Dec 6, 2012
2. Dec 6, 2012