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Conserved generator of a continuous quantum symmetry

If

U (s) = e^{- i s Q /ℏ}

and

U (s)^{†} H U (s) = H

, differentiation at

s = 0

gives

[Q, H] = 0.

In the Heisenberg picture,

\frac{d Q}{d t} = \frac{i}{ℏ} [H, Q] = 0.

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