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The approximations of classical mechanics resulting from quantum mechanicsare richer than a correspondence of classical dynamical variables withself-adjoint Hilbert space operators. Assertion that classical dynamicvariables correspond to self-adjoint Hilbert space operators is disputable andsets unnatural limits on quantum mechanics. Well known examples of classicaldynamical variables not associated with self-adjoint Hilbert space operatorsare discussed as a motivation for the realizations of quantum field theory thatlack Hermitian field operators but exhibit interaction.

Measurement and self-adjoint operators