Heisenberg's relations in discrete \(N\)-dimensional parameterized metric vector spaces (Q1878877)

Heisenberg's uncertainty principle is reviewed within a mathematical framework which looks rather obscure, to say the least. It takes a while until the reader realizes what is meant by a ``discrete \(n\)-dimensional parametrized metric vector space'' (clearly an abuse of language with resulting confusion), namely the Hilbert space \(E\) of functions \(x_i:\mathbb{R}\to\mathbb{C}\) (\(i=1,\dots,n\)) such that \[ \| x\| ^2 =\int \sum_i| x_i(t)| ^2\,dt <\infty. \] A longwinded discussion then leads to a well-known simple fact: the two operators \(t\) and \(d/dt\) on \(E\) satisfy the commutation relation \([d/dt,t]=1\), and hence their covariances, given some state, obey the uncertainty inequality, \(\langle t^2\rangle\langle d^2/dt^2\rangle \geq 1/4\). For its derivation, the expectations are assumed to vanish: \(\langle t\rangle =\langle d/dt\rangle=0\). No relation whatsoever to quantum physics is indicated. In summary, there is nothing to be learned from this text. It is hard to believe that the paper has been scrutinized by some referee.