USSFT Paper VII: Quantum Mechanics Formalism and Ground State Stability: Operators, Commutators, Uncertainty, and the Schrödinger Equation from U-Field Multiplicity

Leonardo Diaz

Published Apr 21, 2026• 0 citations

Abstract

This paper establishes the connection between U-field multiplicity statistics and the formalism of quantum mechanics. We show that when field configurations are weighted by exp(iS_eff/alpha), where S_eff is the on-shell action and alpha is the fundamental coupling constant, the partition function reproduces the Schrodinger equation in the semiclassical limit and the Born rule emerges as a statement about the relative multiplicities of different configurations. The canonical commutation relations [x_hat, p_hat] = i*hbar_eff follow from the uncertainty in defining canonical variables when the effective action has discrete structure. We derive the Robertson uncertainty relation and demonstrate that the full algebra of quantum mechanics arises as a consequence of multiplicity-weighted path statistics on a discrete lattice. This is the seventh paper in the 18-paper USSFT technical series; for the foundational U-field Lagrangian see Papers I-VI, for experimental predictions see Papers XVI-XVII, and for entanglement and Bell correlations see Paper IX.

DOI: 10.5281/zenodo.19675373

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