Finite OS Positivity and Dispersion in a Finite Operator Model

Michael Tomasson, MD

The Osterwalder–Schrader axioms provide a mathematical route from Euclidean structures to Hilbert-space quantum theory, but explicit finite models that can be independently tuned are uncommon. A finite operator model is built from a discrete configuration space obtained via symmetry quotienting and basic counting arguments. Within this setting, three parameters define structurally distinct roles: \alpha_w, interpreted as a temporal stiffness controlling reflection positivity; \tau, an interaction-range parameter governing internal graph connectivity; and g, an interaction coupling that ties spatial propagation to internal degrees of freedom. This separation allow Osterwalder–Schrader positivity to be studied explicitly in finite dimension and reveals that time structure, interaction distance, and coupling strength are logically independent. Stable low-dimensional spectral subspaces are identified with particle-like dispersion properties. This level of structure is observed prior to introducing wave functions, continuum limits, or field-theoretic assumptions.

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