Usually it is pointed out that the relation $[x,p]=i\hbar$ comes from the promoting the poisson bracket to commutator but as I know this process of quantization is called deformation quantization which got it's mathematical foundation in 1960's. I'm not quite sure but I read it in some book that originally Heisenberg came up with the CCR due to the nature radiation. Can anyone enlighten me the real thought process which went in Heisenberg's mind during the conception of CCR?
Also Connes in his noncommutative geometry book shows how one arrives at the CCR since wavelengths of hydrogen spectrum forms a groupoid? Was this the idea behind Heisenberg CCR, did physicists started using group theory in early 20th century?