Manuscript En09-A@1 · En09-A.tex · proposition · eafec9de

Proposition: No finite canonical time commutator

An exact finite stationary realization · lines 780–792 · proof included or linked

En09-A@1#prop:no-ccr

For nonzero finite-dimensional $H_{C}$ , no matrices $T_{C}, H_{C}$ satisfy

[T_{C}, H_{C}] = i ℏ I_{C} .

Proof. The trace of a matrix commutator is zero, whereas the trace of $i ℏ I_{C}$ is $i ℏ dim H_{C} \neq = 0$ .

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