Symbol i

The passage around this formula

They do not commute. The defining fact of the nonrelativistic symmetry group, established by Bargmann and sharpened by Lévy-Leblond, is that its faithful quantum representations require a centrally extended algebra in which $[K_i,P_j]=i\hbar\,m\,\delta_{ij}\,\mathbb 1$. with mass m appearing not as an eigenvalue to be measured state by state but as a fixed number multiplying the identity operator across an entire representation [ 1 , 2 ] . This is what “central” means: the commutator commutes with everything, including $\mathbf K$ and $\mathbf P$ themselves.

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