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  1. $\Mathfrak{D}$ -Differentiation in Hilbert Space and the Structure of Quantum Mechanics Part II: Accelerated Observers and Fictitious Forces. [REVIEW]D. J. Hurley & M. A. Vandyck - 2011 - Foundations of Physics 41 (4):667-685.
    We investigate a possible form of Schrödinger’s equation as it appears to moving observers. It is shown that, in this framework, accelerated motion requires fictitious potentials to be added to the original equation. The gauge invariance of the formulation is established. The example of accelerated Euclidean transformations is treated explicitly, which contain Galilean transformations as special cases. The relationship between an acceleration and a gravitational field is found to be compatible with the picture of the ‘Einstein elevator’. The physical effects (...)
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  • A Minimal Framework for Non-Commutative Quantum Mechanics.D. J. Hurley & M. A. Vandyck - 2014 - Foundations of Physics 44 (11):1168-1187.
    Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.
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