# An algebraic approach to Koopman classical mechanics

@article{Morgan2020AnAA, title={An algebraic approach to Koopman classical mechanics}, author={Peter J Morgan}, journal={Annals of Physics}, year={2020}, volume={414}, pages={168090} }

Abstract Classical mechanics is presented here in a unary operator form, constructed using the binary multiplication and Poisson bracket operations that are given in a phase space formalism, then a Gibbs equilibrium state over this unary operator algebra is introduced, which allows the construction of a Hilbert space as a representation space of a Heisenberg algebra, giving a noncommutative operator algebraic variant of the Koopman–von Neumann approach. In this form, the measurement theory for… CONTINUE READING

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