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Dynamics in the Decompositions Approach to Quantum Mechanics

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Abstract

In Harding (Trans. Amer. Math. Soc. 348(5), 1839–1862 1996) it was shown that the direct product decompositions of any non-empty set, group, vector space, and topological space X form an orthomodular poset Fact X. This is the basis for a line of study in foundational quantum mechanics replacing Hilbert spaces with other types of structures. Here we develop dynamics and an abstract version of a time independent Schrödinger’s equation in the setting of decompositions by considering representations of the group of real numbers in the automorphism group of the orthomodular poset Fact X of decompositions.

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Acknowledgements

The author gratefully acknowledges support of the Foundational Questions Institute grant 2015-144075. The author also thanks Martin Bohata for discussions, and an anonymous referee for helpful suggestions.

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  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    John Harding

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  1. John Harding
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Correspondence to John Harding.

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Harding, J. Dynamics in the Decompositions Approach to Quantum Mechanics. Int J Theor Phys 56, 3971–3990 (2017). https://doi.org/10.1007/s10773-017-3408-5

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  • DOI: https://doi.org/10.1007/s10773-017-3408-5

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