Dynamics in the Decompositions Approach to Quantum Mechanics

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.