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- W4308244674 abstract "We investigate operator algebraic origins of the classical Koopman-von Neumann wave function $psi_{KvN}$ as well as the quantum mechanical one $psi_{QM}$. We introduce a formalism of Operator Mechanics (OM) based on a noncommutative Poisson, symplectic and noncommutative differential structures. OM serves as a pre-quantum algebra from which algebraic structures relevant to real-world classical and quantum mechanics follow. In particular, $psi_{KvN}$ and $psi_{QM}$ are both consequences of this pre-quantum formalism. No a priori Hilbert space is needed. OM admits an algebraic notion of operator expectation values without invoking states. A phase space bundle ${cal E}$ follows from this. $psi_{KvN}$ and $psi_{QM}$ are shown to be sections in ${cal E}$. The difference between $psi_{KvN}$ and $psi_{QM}$ originates from a quantization map interpreted as twisting of sections over ${cal E}$. We also show that the Schr{o}dinger equation is obtained from the Koopman-von Neumann equation. What this suggests is that neither the Schr{o}dinger equation nor the quantum wave function are fundamental structures. Rather, they both originate from a pre-quantum operator algebra. Finally, we comment on how entanglement between these operators suggests emergence of space; and possible extensions of this formalism to field theories." @default.
- W4308244674 created "2022-11-09" @default.
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- W4308244674 date "2022-11-03" @default.
- W4308244674 modified "2023-10-17" @default.
- W4308244674 title "On the Operator Origins of Classical and Quantum Wave Functions" @default.
- W4308244674 doi "https://doi.org/10.48550/arxiv.2211.01838" @default.
- W4308244674 hasPublicationYear "2022" @default.
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